Shapes and angles
By the end of this chapter you will be able to
- Draw a 2-D shape on squared paper and count its sides and corners
- Name a 3-D shape and count its faces, edges and vertices, and say how a 3-D shape looks when it is turned over
- Recognise an angle as a corner of a shape or as a turn
- Name a right angle as a square corner, and name the quarter, half, three-quarter and whole turns by counting right angles
- Say whether an angle is acute (smaller than a right angle) or obtuse (bigger than a right angle)
- Recognise horizontal, vertical, perpendicular and parallel lines
You should already know
- Telling the time and drawing the hands on a clock, including quarter past and half past (Year 2, Chapter 7)
- 2-D and 3-D shapes, and the number of sides of a shape (Year 2, Chapter 8)
- Position and direction, and quarter, half and whole turns (Year 2, Chapter 9)
Where this leads
- Angles measured in degrees, and angles on a straight line and at a point (Year 4 and Year 5)
- Properties of rectangles and the angles and sides of polygons (Year 4 and Year 5)
National Curriculum for England, Key Stage 2 mathematics, Year 3. Content: Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them, Recognise angles as a property of shape or a description of a turn, Identify right angles; recognise that two right angles make a half turn, three make three-quarters of a turn and four a complete turn; identify whether angles are greater or less than a right angle, Identify horizontal and vertical lines and pairs of perpendicular and parallel lines.
Exercise P Do you remember?
Non-calculatorKey words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the straight sides of a triangle.
- Look at the shape name. A triangle is a flat shape with three straight sides and three corners.triangle: 3 sides
- Write the answer. Write the number of sides.3
Check. Three sides and three corners. ✓
Watch out. A side is a straight edge. Do not count the corners as sides.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Think about the shapes you know.
- Look at the picture in your mind. A ball is round in every direction, with no flat faces.ball: round, no flat faces
- Write the answer. The round 3-D shape is a sphere.sphere
Check. A sphere has one curved surface. ✓
Watch out. A cube has flat faces. A ball does not.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 = 4
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.4
Check. Each side starts and ends at a corner, so there are also 4 corners and 4 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns that go all the way round.
- Think of a clock hand. A quarter turn moves the hand from 12 to 3. Four quarter turns bring it back to 12.12 to 3 to 6 to 9 to 12
- Write the answer. It takes four quarter turns to go all the way round.4
Check. Four quarter turns is one whole turn. ✓
Watch out. Do not say 3 or 5. The hand goes round in four equal steps.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Think about a dice or a box with all sides the same.
- Count the faces. A cube has six faces, and all of them are squares.6 square faces
- Write the answer. The shape with six square faces is a cube.cube
Check. A cube has 6 faces, 12 edges and 8 vertices. ✓
Watch out. A cuboid has six faces too, but they are rectangles.
Drawing and counting sides on squared paper
A 2-D shape is flat. It is drawn with straight sides and corners. The shape below is drawn on squared paper. Each small square is one unit, so you can count the squares to find how long a side is.
To draw a shape, put a ruler on two corners and draw along the ruler. Keep going from corner to corner until you join back to the start.
Every side joins two corners. So a shape has the same number of corners as sides.
Key ideas
- A 2-D shape is flat and has straight sides.
- A side is a straight line from one corner to the next.
- A shape has the same number of corners as sides.
- On squared paper, count the squares to measure a side.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 = 5
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.5
Check. Each side starts and ends at a corner, so there are also 5 corners and 5 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Method. Count the squares in one row, count the rows, then multiply.
- Count the squares along the bottom. Each small square is one unit. Count them in one row.5 squares along
- Count the rows. Count how many rows of squares go up the shape.2 rows
- Multiply the rows by the squares in each row. Every row has the same number of squares, so multiply.5 × 2 = 10
- Write the answer. Write the total number of squares.10
Check. Adding 5 squares, 2 times, gives 10 squares. ✓
Watch out. Count every square inside the shape, not only the squares on the edge.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EF, FA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 + 1 = 6
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.6
Check. Each side starts and ends at a corner, so there are also 6 corners and 6 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Watch out
Watch out: count the sides, not the squares. A side can be 5 squares long, but it is still only one side.
Exam tip
Grown-up tip. Ask your child to draw a triangle and a square on squared paper with a ruler. Then ask: "How many sides? How many corners? How many squares long is the bottom side?"
Exercise 8A Sides, corners and squares on a grid
Non-calculatorKey words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 = 3
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.3
Check. Each side starts and ends at a corner, so there are also 3 corners and 3 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 = 4
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.4
Check. Each side starts and ends at a corner, so there are also 4 corners and 4 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 = 5
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.5
Check. Each side starts and ends at a corner, so there are also 5 corners and 5 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EF, FA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 + 1 = 6
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.6
Check. Each side starts and ends at a corner, so there are also 6 corners and 6 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Find the side and count the small squares along it.
- Find the side. The side goes from corner A to corner B.A to B
- Count the squares along it. Each small square is one unit, so count the squares along the side.5 squares
- Write the answer. Write the number of squares.5
Check. Count back from B to A: still 5 squares. ✓
Watch out. Count the squares, not the corners. A side that is 5 squares long has 5 squares along it.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 = 3
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.3
Check. Each side starts and ends at a corner, so there are also 3 corners and 3 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 = 3
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.3
Check. Each side starts and ends at a corner, so there are also 3 corners and 3 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Look at the shape. It has three sides and three corners, like a slice of cake.
- Look at the shape. It has three straight sides.3 sides
- Use the name. A shape with three straight sides is a triangle.three sides = triangle
- Write the answer. Write the name of the shape.triangle
Check. Three sides, so triangle. ✓
Watch out. Tri means three. A triangle has three sides and three corners.
Method. Count the squares in one row, count the rows, then multiply.
- Count the squares along the bottom. Each small square is one unit. Count them in one row.3 squares along
- Count the rows. Count how many rows of squares go up the shape.3 rows
- Multiply the rows by the squares in each row. Every row has the same number of squares, so multiply.3 × 3 = 9
- Write the answer. Write the total number of squares.9
Check. Adding 3 squares, 3 times, gives 9 squares. ✓
Watch out. Count every square inside the shape, not only the squares on the edge.
Method. Count the squares in one row, count the rows, then multiply.
- Count the squares along the bottom. Each small square is one unit. Count them in one row.4 squares along
- Count the rows. Count how many rows of squares go up the shape.2 rows
- Multiply the rows by the squares in each row. Every row has the same number of squares, so multiply.4 × 2 = 8
- Write the answer. Write the total number of squares.8
Check. Adding 4 squares, 2 times, gives 8 squares. ✓
Watch out. Count every square inside the shape, not only the squares on the edge.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Use the name of the shape. Penta means five.
- Look at the name. The first part of pentagon, penta, means five.penta = 5
- Count the sides. A pentagon has five straight sides and five corners.5 sides
- Write the answer. Write the number of sides.5
Check. Five sides, and five corners too. ✓
Watch out. Hexa means six, so a hexagon has six sides.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the sides of the hexagon, then compare with what Ben says.
- Count the sides. Go round the outside once, and count each straight side.6 sides
- Compare with Ben. Ben says 6 sides, which is the same as the count.6 = 6
- Write the answer. Ben is right.Yes
Check. The hexagon has 6 sides, so Ben is right. ✓
Watch out. Count each side once, and check the last side joins back to the first corner.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Think about other shapes that also have 4 sides.
- Look at what we know. The shape has 4 sides and 4 corners. A square has this too.4 sides, 4 corners
- Find another shape. A rectangle that is 5 squares long and 2 squares high also has 4 sides and 4 corners, but its sides are not all the same length.rectangle 5 by 2: 4 sides
- Write the answer. Ellie is not right, because the shape could be a rectangle.No
Check. Some shapes with 4 sides are squares, and some are rectangles. ✓
Watch out. Four sides and four corners is not enough to name a shape. Check whether the sides are all the same length.
Making and describing 3-D shapes
A 3-D shape is solid, and it takes up space. It has faces, edges and vertices.
A face is one flat or curved surface. An edge is a straight line where two faces meet. A vertex is a corner.
If you turn a 3-D shape over, or lay it on its side, it is still the same shape. Only its position has changed. A cylinder lying on its side is still a cylinder.
Key ideas
- A 3-D shape is solid. Its faces can be flat or curved.
- An edge is a straight line where two faces meet.
- A vertex is a corner. A straw makes one edge, and a clay ball makes one vertex.
- Turning a 3-D shape does not change its name.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has six flat faces, and they are rectangles. It has straight edges and corners.6 flat faces
- Match the shape to its name. Use the name that fits the faces.cuboid
- Write the answer. Write the name of the shape.cuboid
Check. The name cuboid fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Sam needs one straw for each edge. Count the edges of a square-based pyramid.
- Find the shape. Use the name of the shape, or the picture.square-based pyramid
- Count the edges. Each straw is one edge. Count the straight edges, where two faces meet.edges = 8
- Write the answer. Write the number.8
Check. Each straw is one edge, so a square-based pyramid needs 8 straws. ✓
Watch out. Count each straight edge once. Two faces meet at each edge, so do not count it again from the other face.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Count the flat faces of the triangular prism.
- Find the shape. Use the name of the shape, or the picture.triangular prism
- Count the flat faces. Count each flat face once. Do not count the curved surface.flat faces = 5
- Write the answer. Write the number.5
Check. Count the flat faces again on the picture or the name: still 5. ✓
Watch out. Count each flat face once. Curved surfaces are not flat faces.
Watch out
Watch out: a cylinder has curved faces, but it is still a 3-D shape with flat faces too. A sphere has no flat faces and no edges at all. Do not say a sphere is a cube.
Exam tip
Grown-up tip. Look at a cereal box at home. It is a cuboid with six flat faces. Ask: "How many edges? How many vertices?" Then turn the box on its side and ask, "Is it still the same shape?"
Exercise 8B Naming and counting 3-D shapes
Non-calculatorKey words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has six flat faces, and they are rectangles. It has straight edges and corners.6 flat faces
- Match the shape to its name. Use the name that fits the faces.cuboid
- Write the answer. Write the name of the shape.cuboid
Check. The name cuboid fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has one square face at the bottom, and four triangle faces that meet at a point at the top.5 flat faces
- Match the shape to its name. Use the name that fits the faces.square-based pyramid
- Write the answer. Write the name of the shape.square-based pyramid
Check. The name square-based pyramid fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has two flat circle faces at the ends, and one curved face round the middle.2 flat faces
- Match the shape to its name. Use the name that fits the faces.cylinder
- Write the answer. Write the name of the shape.cylinder
Check. The name cylinder fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has one curved surface and no flat faces. It is shaped like a ball.0 flat faces
- Match the shape to its name. Use the name that fits the faces.sphere
- Write the answer. Write the name of the shape.sphere
Check. The name sphere fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has two triangle faces at the ends, and three rectangle faces along its sides.5 flat faces
- Match the shape to its name. Use the name that fits the faces.triangular prism
- Write the answer. Write the name of the shape.triangular prism
Check. The name triangular prism fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Each straw makes one edge. Count the edges of a cube.
- Find the shape. Use the name of the shape, or the picture.cube
- Count the edges. Each straw is one edge. Count the straight edges, where two faces meet.edges = 12
- Write the answer. Write the number.12
Check. Each straw is one edge, so a cube needs 12 straws. ✓
Watch out. Count each straight edge once. Two faces meet at each edge, so do not count it again from the other face.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Each straw makes one edge. Count the edges of a triangular prism.
- Find the shape. Use the name of the shape, or the picture.triangular prism
- Count the edges. Each straw is one edge. Count the straight edges, where two faces meet.edges = 9
- Write the answer. Write the number.9
Check. Each straw is one edge, so a triangular prism needs 9 straws. ✓
Watch out. Count each straight edge once. Two faces meet at each edge, so do not count it again from the other face.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Count the vertices of the square-based pyramid.
- Find the shape. Use the name of the shape, or the picture.square-based pyramid
- Count the vertices. A vertex is a corner. Count each corner once.vertices = 5
- Write the answer. Write the number.5
Check. Count the vertices again on the picture or the name: still 5. ✓
Watch out. Count each corner once. Do not count the same corner twice.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Count the flat faces of the cuboid.
- Find the shape. Use the name of the shape, or the picture.cuboid
- Count the flat faces. Count each flat face once. Do not count the curved surface.flat faces = 6
- Write the answer. Write the number.6
Check. Count the flat faces again on the picture or the name: still 6. ✓
Watch out. Count each flat face once. Curved surfaces are not flat faces.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Count the flat faces on each shape. The shape with none is the answer.
- Look at shape A. A cylinder has two flat circle faces, one at each end.A: 2 flat faces
- Look at shape B. A cone has one flat circle face at the bottom.B: 1 flat face
- Look at shape C. A sphere has no flat faces, only a curved surface.C: 0 flat faces
- Write the answer. Shape C has no flat faces.C
Check. A ball has no flat faces, so it is shape C. ✓
Watch out. A cone and a cylinder both have flat faces, so they are not the answer.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Find the straws for two prisms. Each prism needs the same number of straws as its edges.
- Find the straws for one prism. A triangular prism has 9 edges, so it needs 9 straws.1 prism = 9 straws
- Multiply by 2. Two prisms need two lots of 9 straws.2 × 9 = 18
- Write the answer. Ella uses this many straws.18
Check. 9 + 9 = 18. ✓
Watch out. Multiply by 2 for two shapes. Do not add 2 to 9.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Take the straws she used away from the straws she had.
- Find the straws she had. Ella starts with 30 straws.start = 30 straws
- Take away the straws she used. Subtract the straws in the two prisms.30 − 18 = 12
- Write the answer. This many straws are left.12
Check. 18 + 12 = 30. ✓
Watch out. Take away what she used. Do not add.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Think about what changes when a shape is turned over.
- Think about the shape. Turning or laying a shape on its side only changes its position. It is still the same shape.same shape, new position
- Check the faces. The lying cylinder still has two flat circle faces and one curved face.2 flat faces + 1 curved face
- Write the answer. Sam is not right. It is still a cylinder.No
Check. Its faces and its name do not change when it is turned. ✓
Watch out. Turning a shape changes where its faces point, not what the shape is.
Angles as corners and as turns
An angle is made where two straight lines meet. The two lines are the arms. The point where they meet is the vertex.
Every corner of a shape is an angle. So a shape has the same number of angles as it has corners. A triangle has 3 angles, and a square has 4.
An angle can also describe a turn. When a hand moves round a clock, it turns through an angle. The bigger the turn, the more the hand has moved.
Key ideas
- An angle is made where two lines (the arms) meet at a point (the vertex).
- Every corner of a shape is an angle.
- An angle can describe a turn, such as the turn of a hand.
- Later we will compare angles with a square corner.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the angles. Each corner of the shape is one angle.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 = 3
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.3
Check. Each side starts and ends at a corner, so there are also 3 corners and 3 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 = 1 quarter turn
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.1 quarter turn = quarter turn
- Write the answer. Write the name of the turn.quarter turn
Check. quarter turn: 1 right angle, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the angles. Each corner of the shape is one angle.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EF, FA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 + 1 = 6
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.6
Check. Each side starts and ends at a corner, so there are also 6 corners and 6 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Watch out
Watch out: the length of the arms does not change the size of the angle. Two angles can have arms of different lengths and still be the same angle. Look at how far the arms are opened.
Exam tip
Grown-up tip. Ask your child to find corners in the room: a door, a book, a table. Ask: "Is each corner an angle? How many angles does the table have?" Then ask them to turn a clock hand from 12 to 6.
Exercise 8C Angles in shapes and turns
Non-calculatorKey words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the angles. Each corner of the shape is one angle.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 = 4
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.4
Check. Each side starts and ends at a corner, so there are also 4 corners and 4 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the angles. Each corner of the shape is one angle.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 = 5
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.5
Check. Each side starts and ends at a corner, so there are also 5 corners and 5 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the angles. Each corner of the shape is one angle.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EF, FA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 + 1 = 6
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.6
Check. Each side starts and ends at a corner, so there are also 6 corners and 6 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 = 1 quarter turn
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.1 quarter turn = quarter turn
- Write the answer. Write the name of the turn.quarter turn
Check. quarter turn: 1 right angle, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 = 2 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.2 quarter turns = half turn
- Write the answer. Write the name of the turn.half turn
Check. half turn: 2 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 + 1 = 3 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.3 quarter turns = three-quarter turn
- Write the answer. Write the name of the turn.three-quarter turn
Check. three-quarter turn: 3 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 + 1 + 1 = 4 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.4 quarter turns = whole turn
- Write the answer. Write the name of the turn.whole turn
Check. whole turn: 4 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. An angle is made where two lines meet. The lines are the arms. The point where they meet is the vertex.
Method. Count the angles of each shape, then add them together.
- Count the angles in the triangle. A triangle has 3 corners, so it has 3 angles.triangle: 3 angles
- Count the angles in the rectangle. A rectangle has 4 corners, so it has 4 angles.rectangle: 4 angles
- Add them together. Add the two numbers.3 + 4 = 7
- Write the answer. The total number of angles is the answer.7
Check. 7 - 4 = 3, the triangle. ✓
Watch out. Add the angles of the two shapes. Do not add the sides of one shape.
Key words. An angle is made where two lines meet. The lines are the arms. The point where they meet is the vertex.
Method. Count the angles of each shape, then say which number is bigger.
- Count the angles of the hexagon. A hexagon has six corners.hexagon: 6
- Count the angles of the pentagon. A pentagon has five corners.pentagon: 5
- Compare the numbers. The bigger number of angles is the shape with more angles.6 > 5
- Write the answer. Write the name of the shape with more angles.hexagon
Check. Hexagon 6, pentagon 5. ✓
Watch out. Read the names carefully. Hexa is six and penta is five.
Key words. An angle is made where two lines meet. The lines are the arms. The point where they meet is the vertex.
Method. Count the sides and corners, and remember that every corner is an angle.
- Count the sides of the shape. Ali says the shape has 6 sides.6 sides
- Count the angles. A shape has one angle at each corner, and the same number of corners as sides.6 corners = 6 angles
- Write the answer. The shape has 6 angles, not 5. Ali is not right.No
Check. 6 sides means 6 corners, so 6 angles. ✓
Watch out. Each side ends at a corner, so count the corners as well.
Key words. An angle is made where two lines meet. The lines are the arms. The point where they meet is the vertex.
Method. Think about the two arms and the vertex in the turn.
- Look at the turn. The hand is one arm, its start is the other arm, and the centre is the vertex.two arms, one vertex
- Decide if it is an angle. The space between the arms is an angle. A turn is an angle.turn = angle
- Write the answer. Ruby is not right. A turn is an angle.No
Check. A turn of a hand is described by an angle. ✓
Watch out. An angle does not need a corner on a shape. It can be a turn.
Right angles and turns
A right angle is a square corner. The corner of a page, a book or a table is a right angle.
A quarter turn makes one right angle. Two right angles make a half turn. Three right angles make a three-quarter turn. Four right angles make a whole turn, which takes you all the way back to the start.
Key ideas
- A right angle is a square corner.
- A quarter turn is one right angle.
- Two right angles make a half turn.
- Three right angles make a three-quarter turn.
- Four right angles make a whole turn.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.half turn = 2 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 = 2
- Write the answer. The answer is the number of right angles.2
Check. half turn: 2 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: right, C: right, D: right
- Pick out the right angles. Count the corners that are a square corner.1 + 1 + 1 + 1 = 4
- Write the answer. Write how many corners are of this kind.4
Check. Right 4, acute 0 and obtuse 0 make 4 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 + 1 = 3 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.3 quarter turns = three-quarter turn
- Write the answer. Write the name of the turn.three-quarter turn
Check. three-quarter turn: 3 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Watch out
Watch out: three right angles do not make a half turn. Two right angles make a half turn. Count the quarter turns: one, two, three, four, and then you are back at the start.
Exam tip
Grown-up tip. Stand facing the wall. Turn a quarter turn to the right, then another. Ask: "How many quarter turns make a half turn? How many make a whole turn?" Use the corner of a book to check each right angle.
Exercise 8D Right angles and turns
Non-calculatorKey words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.whole turn = 4 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 + 1 + 1 = 4
- Write the answer. The answer is the number of right angles.4
Check. whole turn: 4 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.quarter turn = 1 quarter turn
- Count the right angles in the turn. Each quarter turn is one right angle.1 = 1
- Write the answer. The answer is the number of right angles.1
Check. quarter turn: 1 right angle. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.three-quarter turn = 3 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 + 1 = 3
- Write the answer. The answer is the number of right angles.3
Check. three-quarter turn: 3 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 + 1 + 1 = 4 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.4 quarter turns = whole turn
- Write the answer. Write the name of the turn.whole turn
Check. whole turn: 4 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 = 2 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.2 quarter turns = half turn
- Write the answer. Write the name of the turn.half turn
Check. half turn: 2 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: right, C: right, D: right
- Pick out the right angles. Count the corners that are a square corner.1 + 1 + 1 + 1 = 4
- Write the answer. Write how many corners are of this kind.4
Check. Right 4, acute 0 and obtuse 0 make 4 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: acute, C: acute
- Pick out the right angles. Count the corners that are a square corner.1 = 1
- Write the answer. Write how many corners are of this kind.1
Check. Right 1, acute 2 and obtuse 0 make 3 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: acute, B: right, C: right, D: obtuse
- Pick out the right angles. Count the corners that are a square corner.1 + 1 = 2
- Write the answer. Write how many corners are of this kind.2
Check. Right 2, acute 1 and obtuse 1 make 4 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.half turn = 2 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 = 2
- Write the answer. The answer is the number of right angles.2
Check. half turn: 2 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the quarter turns, then use the name for that many.
- Count the quarter turns. Each quarter turn is one right angle, and one quarter of a whole turn.1 + 1 = 2 quarter turns
- Name the turn. One quarter turn is a quarter. Two make a half turn, three make a three-quarter turn, and four make a whole turn.2 quarter turns = half turn
- Write the answer. Write the name of the turn.half turn
Check. half turn: 2 right angles, and four right angles make a whole turn. ✓
Watch out. Three quarter turns is not a half turn. A half turn is two quarter turns.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Count the right angles in a half turn, then compare with three right angles.
- Count the right angles in a half turn. A half turn is two right angles.2 right angles
- Count the right angles that Mia says. Mia says three right angles make a half turn.3 right angles
- Compare. Three right angles is one more than a half turn. Three right angles make a three-quarter turn.3 > 2, so 3 is not a half turn
- Write the answer. Mia is not right.No
Check. half turn is 2 right angles. ✓
Watch out. Two right angles make a half turn, not three.
Acute and obtuse angles
Some angles are smaller than a right angle. These are acute angles. They look sharp and narrow.
An angle that is exactly a square corner is a right angle.
Some angles are bigger than a right angle, but smaller than a half turn. These are obtuse angles. They look blunt and wide.
To decide, compare the angle with the corner of a square. Do not look at how long the arms are.
Key ideas
- An acute angle is smaller than a right angle.
- A right angle is exactly a square corner.
- An obtuse angle is bigger than a right angle and smaller than a half turn.
- Compare the angle with the corner of a square.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened less than a square corner, so the angle is smaller.acute angle
- Write the answer. Write the type of angle.acute
Check. An acute angle is smaller than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened wider than a square corner, so the angle is bigger.obtuse angle
- Write the answer. Write the type of angle.obtuse
Check. An obtuse angle is bigger than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: acute, B: acute, C: obtuse
- Pick out the obtuse angles. Count the corners that are bigger than a square corner.1 = 1
- Write the answer. Write how many corners are of this kind.1
Check. Right 0, acute 2 and obtuse 1 make 3 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Watch out
Watch out: a long arm does not make an angle bigger. An angle with long arms can still be acute, if the arms open only a little.
Exam tip
Grown-up tip. Join two straws with a paper clip, and open them into an angle. Put the corner of a piece of paper into the angle. Ask: "Is it smaller or bigger than the corner of the paper?"
Exercise 8E Acute, right and obtuse angles
Non-calculatorKey words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened less than a square corner, so the angle is smaller.acute angle
- Write the answer. Write the type of angle.acute
Check. An acute angle is smaller than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened wider than a square corner, so the angle is bigger.obtuse angle
- Write the answer. Write the type of angle.obtuse
Check. An obtuse angle is bigger than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms make a square corner, the same as the corner of a square.right angle
- Write the answer. Write the type of angle.right
Check. A right angle is exactly the same as a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened less than a square corner, so the angle is smaller.acute angle
- Write the answer. Write the type of angle.acute
Check. An acute angle is smaller than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened wider than a square corner, so the angle is bigger.obtuse angle
- Write the answer. Write the type of angle.obtuse
Check. An obtuse angle is bigger than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare every angle with a square corner, then choose the letter of the one that is asked for.
- Compare each angle with the corner of a square. Smaller than a square corner is acute. Bigger is obtuse. The same is right.A is obtuse, B is acute, C is right
- Find the acute angle. Only one of the angles is this kind.B is acute
- Write the letter. Write the letter of that angle.B
Check. The other angles are not acute. ✓
Watch out. Look at the opening between the arms, not at their length.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare every angle with a square corner, then choose the letter of the one that is asked for.
- Compare each angle with the corner of a square. Smaller than a square corner is acute. Bigger is obtuse. The same is right.A is acute, B is obtuse, C is acute
- Find the obtuse angle. Only one of the angles is this kind.B is obtuse
- Write the letter. Write the letter of that angle.B
Check. The other angles are not obtuse. ✓
Watch out. Look at the opening between the arms, not at their length.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: acute, B: acute, C: acute
- Pick out the acute angles. Count the corners that are smaller than a square corner.1 + 1 + 1 = 3
- Write the answer. Write how many corners are of this kind.3
Check. Right 0, acute 3 and obtuse 0 make 3 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: obtuse, B: obtuse, C: right, D: obtuse, E: obtuse, F: right
- Pick out the obtuse angles. Count the corners that are bigger than a square corner.1 + 1 + 1 + 1 = 4
- Write the answer. Write how many corners are of this kind.4
Check. Right 2, acute 0 and obtuse 4 make 6 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: right, C: obtuse, D: obtuse, E: obtuse
- Pick out the acute angles. Count the corners that are smaller than a square corner.0 corners of this kind
- Write the answer. Write how many corners are of this kind.0
Check. Right 2, acute 0 and obtuse 3 make 5 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: right, C: obtuse, D: obtuse, E: obtuse
- Pick out the right angles. Count the corners that are a square corner.1 + 1 = 2
- Write the answer. Write how many corners are of this kind.2
Check. Right 2, acute 0 and obtuse 3 make 5 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: right, C: obtuse, D: obtuse, E: obtuse
- Pick out the obtuse angles. Count the corners that are bigger than a square corner.1 + 1 + 1 = 3
- Write the answer. Write how many corners are of this kind.3
Check. Right 2, acute 0 and obtuse 3 make 5 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the corner of the book with the corner of a square.
- Look at the corner of the book. A book has square corners, the same as a square.book corner = square corner
- Name the angle. A square corner is a right angle. An obtuse angle is bigger than a right angle.right angle, not obtuse
- Write the answer. Ali is not right. The corner of a book is a right angle.No
Check. A square corner is a right angle. ✓
Watch out. Obtuse angles are wider than a square corner. A book corner is not wider.
Horizontal, vertical, perpendicular and parallel lines
A horizontal line goes straight across, flat like the floor.
A vertical line goes straight up and down, like a wall or a flagpole.
Perpendicular lines meet at a right angle, which is a square corner.
Parallel lines have the same direction. They never meet, and they stay the same distance apart.
Key ideas
- Horizontal: across, flat like the floor.
- Vertical: up and down, like a wall.
- Perpendicular: lines that meet at a right angle.
- Parallel: lines that never meet and stay the same distance apart.
- Horizontal and vertical lines are perpendicular to each other.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is horizontal.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.A is horizontal, B is vertical, C is slanted
- Find the horizontal line. This line is flat across the page.A is horizontal
- Write the letter. Write the letter of that line.A
Check. The other lines are not horizontal. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check every pair of lines. Choose the pair that is perpendicular.
- Check each pair of lines. Look at the direction of each line, and whether the lines cross.A and B: perpendicular, A and C: neither, B and C: neither
- Find the perpendicular pair. They cross at a square corner, a right angle.A and B are perpendicular
- Write the answer. Write the two letters.A and B
Check. No other pair is perpendicular. ✓
Watch out. Lines that look close together are not always parallel. Check the direction of each line.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check every pair of lines. Choose the pair that is parallel.
- Check each pair of lines. Look at the direction of each line, and whether the lines cross.A and B: parallel, A and C: neither, B and C: neither
- Find the parallel pair. They have the same direction and never meet.A and B are parallel
- Write the answer. Write the two letters.A and B
Check. No other pair is parallel. ✓
Watch out. Lines that look close together are not always parallel. Check the direction of each line.
Watch out
Watch out: lines do not have to be horizontal or vertical to be perpendicular or parallel. Two slanted lines can be parallel, and two slanted lines can be perpendicular. Check the direction of each line.
Exam tip
Grown-up tip. Use a ruler and a square corner of paper. Ask your child to find a horizontal line, a vertical line, and two lines that are perpendicular in the room, such as the edge of a table and the edge of a door.
Exercise 8F Horizontal, vertical, perpendicular and parallel lines
Non-calculatorKey words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is vertical.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.A is horizontal, B is vertical, C is slanted
- Find the vertical line. This line is straight up and down.B is vertical
- Write the letter. Write the letter of that line.B
Check. The other lines are not vertical. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is slanted.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.A is horizontal, B is vertical, C is slanted
- Find the slanted line. This line is sloping.C is slanted
- Write the letter. Write the letter of that line.C
Check. The other lines are not slanted. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is vertical.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.A is slanted, B is slanted, C is vertical
- Find the vertical line. This line is straight up and down.C is vertical
- Write the letter. Write the letter of that line.C
Check. The other lines are not vertical. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. List every pair of lines once, then count the pairs that are perpendicular.
- List every pair of lines. Take each pair once.P and Q, P and R, P and S, Q and R, Q and S, R and S
- Keep the pairs that are perpendicular. Count only the pairs that are perpendicular.P and S, Q and R
- Write the answer. Write how many pairs there are.2
Check. 6 pairs were checked in all. ✓
Watch out. Count each pair once. A and B is the same pair as B and A.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check whether the two lines have the same direction.
- Look at each line. Line A is slanted. Line C is horizontal.A: slanted; C: horizontal
- Check the direction. Parallel lines have the same direction. These two do not.different directions
- Write the answer. Lines A and C are not parallel.No
Check. Parallel lines never meet, but lines A and C cross. ✓
Watch out. Parallel means the same direction, not just close together.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is horizontal.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.P is slanted, Q is horizontal, R is vertical
- Find the horizontal line. This line is flat across the page.Q is horizontal
- Write the letter. Write the letter of that line.Q
Check. The other lines are not horizontal. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is vertical.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.P is slanted, Q is horizontal, R is vertical
- Find the vertical line. This line is straight up and down.R is vertical
- Write the letter. Write the letter of that line.R
Check. The other lines are not vertical. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. List every pair of lines once, then count the pairs that are parallel.
- List every pair of lines. Take each pair once.A and B, A and C, B and C
- Keep the pairs that are parallel. Count only the pairs that are parallel.A and B
- Write the answer. Write how many pairs there are.1
Check. 3 pairs were checked in all. ✓
Watch out. Count each pair once. A and B is the same pair as B and A.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Think about what two horizontal lines look like.
- Look at the direction. Both lines go straight across, so they have the same direction.same direction
- Think about where they meet. Two flat lines at different heights never meet, and they stay the same distance apart.never meet, same distance
- Write the answer. This is true.Yes
Check. Parallel lines have the same direction and never meet. ✓
Watch out. Two horizontal lines at the same height are the same line.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Picture a vertical line and a horizontal line that cross.
- Look at their directions. One goes up and down, and the other goes across.up-down and across
- Look at where they meet. Where they cross, they make a square corner, which is a right angle.square corner = right angle
- Write the answer. Ella is right. They are perpendicular.Yes
Check. Horizontal and vertical lines always meet at a right angle. ✓
Watch out. Perpendicular lines meet at a square corner.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Compare the direction of a horizontal line with a slanted line.
- Look at the direction of the horizontal line. A horizontal line goes straight across.across
- Look at the direction of the slanted line. A slanted line slopes, so it goes a different way.sloping
- Write the answer. Their directions are different, so they are not parallel.No
Check. Parallel lines have the same direction. ✓
Watch out. A horizontal line and a slanted line have different directions, so they can never be parallel.
Chapter summary
| Skill | Method |
|---|---|
| 2-D shapes | Count the sides and the corners. A shape has the same number of corners as sides, and the same number of angles. |
| 3-D shapes | Faces can be flat or curved. An edge is a straight line where two faces meet. A vertex is a corner. |
| Angles | An angle is made where two lines meet. Every corner of a shape is an angle, and an angle can also be a turn. |
| Right angles and turns | A quarter turn is one right angle. Two make a half turn, three make a three-quarter turn, and four make a whole turn. |
| Acute and obtuse angles | Acute is smaller than a right angle. Obtuse is bigger than a right angle. Compare with a square corner. |
| Horizontal, vertical, perpendicular and parallel | Horizontal goes across. Vertical goes up and down. Perpendicular lines meet at a right angle. Parallel lines never meet. |
Can you…?
- I can draw a 2-D shape on squared paper, and count its sides and corners.
- I can name a 3-D shape, and count its faces, edges and vertices.
- I know that an angle is made where two lines meet, and that a turn can be an angle.
- I know a right angle is a square corner, and I can count right angles.
- I know that two right angles make a half turn, and four make a whole turn.
- I can say whether an angle is acute, right or obtuse, by comparing it with a square corner.
- I can name horizontal, vertical, perpendicular and parallel lines.
Key terms
- 2-D shape
- A flat shape with straight sides, such as a triangle or a square.
- 3-D shape
- A solid shape that takes up space, such as a cube or a ball.
- Face
- A flat or curved surface of a 3-D shape.
- Edge
- A straight line where two faces of a 3-D shape meet.
- Vertex
- A corner of a 3-D shape or a 2-D shape. There are several vertices.
- Angle
- The space between two lines (the arms) that meet at a point (the vertex). A turn can also be an angle.
- Right angle
- A square corner, such as the corner of a page.
- Acute angle
- An angle that is smaller than a right angle.
- Obtuse angle
- An angle that is bigger than a right angle but smaller than a half turn.
- Horizontal
- A line that goes straight across, flat like the floor.
- Vertical
- A line that goes straight up and down, like a wall.
- Perpendicular
- Two lines that meet at a right angle.
- Parallel
- Two lines that have the same direction, never meet and stay the same distance apart.
Exercise 8Z Check-up
Non-calculatorKey words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has one flat circle face at the bottom, and one curved face that comes up to a point.1 flat face
- Match the shape to its name. Use the name that fits the faces.cone
- Write the answer. Write the name of the shape.cone
Check. The name cone fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 = 5
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.5
Check. Each side starts and ends at a corner, so there are also 5 corners and 5 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: right, B: acute, C: acute
- Pick out the acute angles. Count the corners that are smaller than a square corner.1 + 1 = 2
- Write the answer. Write how many corners are of this kind.2
Check. Right 1, acute 2 and obtuse 0 make 3 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened wider than a square corner, so the angle is bigger.obtuse angle
- Write the answer. Write the type of angle.obtuse
Check. An obtuse angle is bigger than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Look at the direction of each line. Choose the one that is horizontal.
- Look at each line. A horizontal line goes across. A vertical line goes straight up and down. A slanted line slopes.P is slanted, Q is vertical, R is horizontal, S is slanted
- Find the horizontal line. This line is flat across the page.R is horizontal
- Write the letter. Write the letter of that line.R
Check. The other lines are not horizontal. ✓
Watch out. A slanted line is not horizontal or vertical, even when it is nearly flat.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Each straw makes one edge. Count the edges of a cuboid.
- Find the shape. Use the name of the shape, or the picture.cuboid
- Count the edges. Each straw is one edge. Count the straight edges, where two faces meet.edges = 12
- Write the answer. Write the number.12
Check. Each straw is one edge, so a cuboid needs 12 straws. ✓
Watch out. Count each straight edge once. Two faces meet at each edge, so do not count it again from the other face.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.half turn = 2 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 = 2
- Write the answer. The answer is the number of right angles.2
Check. half turn: 2 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Count the corners. Each corner is where two sides meet.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CD, DE, EF, FA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 + 1 + 1 + 1 = 6
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.6
Check. Each side starts and ends at a corner, so there are also 6 corners and 6 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check every pair of lines. Choose the pair that is perpendicular.
- Check each pair of lines. Look at the direction of each line, and whether the lines cross.P and Q: neither, P and R: neither, Q and R: perpendicular
- Find the perpendicular pair. They cross at a square corner, a right angle.Q and R are perpendicular
- Write the answer. Write the two letters.Q and R
Check. No other pair is perpendicular. ✓
Watch out. Lines that look close together are not always parallel. Check the direction of each line.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare every angle with a square corner, then choose the letter of the one that is asked for.
- Compare each angle with the corner of a square. Smaller than a square corner is acute. Bigger is obtuse. The same is right.A is obtuse, B is acute, C is obtuse
- Find the acute angle. Only one of the angles is this kind.B is acute
- Write the letter. Write the letter of that angle.B
Check. The other angles are not acute. ✓
Watch out. Look at the opening between the arms, not at their length.
Total 18 marks. Allow about 18 minutes.
Exercise 8X Practice test questions
Non-calculatorKey words. A side is a straight edge of a 2-D shape. A corner is where two sides meet. A shape has the same number of corners as sides.
Method. Go round the outside of the shape. Count each straight side once.
- Go round the outside. Start at one corner and follow each straight side to the next corner.AB, BC, CA
- Count them. Count each one once. Do not count a side again when you come back to it.1 + 1 + 1 = 3
- Write the answer. A shape has the same number of corners as sides, so the number of angles is the same too.3
Check. Each side starts and ends at a corner, so there are also 3 corners and 3 angles. ✓
Watch out. Count each side once, not twice. Count the corners in the same way.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Look at the faces, then choose the name.
- Look at the faces. It has two triangle faces at the ends, and three rectangle faces along its sides.5 flat faces
- Match the shape to its name. Use the name that fits the faces.triangular prism
- Write the answer. Write the name of the shape.triangular prism
Check. The name triangular prism fits the faces and the shape in the picture. ✓
Watch out. A ball has no flat faces, so it is not a cube or a cylinder.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.half turn = 2 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 = 2
- Write the answer. The answer is the number of right angles.2
Check. half turn: 2 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare the angle with a square corner. Smaller is acute, bigger is obtuse, and the same is right.
- Compare the angle with the corner of a square. Put a square corner of paper into the angle to check.square corner = right angle
- Look at the opening between the arms. The arms are opened wider than a square corner, so the angle is bigger.obtuse angle
- Write the answer. Write the type of angle.obtuse
Check. An obtuse angle is bigger than a square corner. ✓
Watch out. Do not judge the angle by the length of its arms. Only the opening between the arms matters.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check every pair of lines. Choose the pair that is perpendicular.
- Check each pair of lines. Look at the direction of each line, and whether the lines cross.A and B: perpendicular, A and C: neither, B and C: neither
- Find the perpendicular pair. They cross at a square corner, a right angle.A and B are perpendicular
- Write the answer. Write the two letters.A and B
Check. No other pair is perpendicular. ✓
Watch out. Lines that look close together are not always parallel. Check the direction of each line.
Key words. A face is a flat or curved surface of a 3-D shape. An edge is a straight line where two faces meet. A vertex is a corner. There are several vertices.
Method. Count the vertices of the cuboid.
- Find the shape. Use the name of the shape, or the picture.cuboid
- Count the vertices. A vertex is a corner. Count each corner once.vertices = 8
- Write the answer. Write the number.8
Check. Count the vertices again on the picture or the name: still 8. ✓
Watch out. Count each corner once. Do not count the same corner twice.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: acute, B: acute, C: obtuse
- Pick out the acute angles. Count the corners that are smaller than a square corner.1 + 1 = 2
- Write the answer. Write how many corners are of this kind.2
Check. Right 0, acute 2 and obtuse 1 make 3 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A turn is how far something has moved round. A half turn is two right angles. A whole turn is four right angles.
Method. Each quarter turn is one right angle, so count the quarter turns.
- Look at the turn. Find out how many quarter turns it is made of.three-quarter turn = 3 quarter turns
- Count the right angles in the turn. Each quarter turn is one right angle.1 + 1 + 1 = 3
- Write the answer. The answer is the number of right angles.3
Check. three-quarter turn: 3 right angles. ✓
Watch out. Count quarter turns, not whole turns. A half turn has 2 right angles, not 1.
Key words. A right angle is a square corner, like the corner of a page. A quarter turn makes one right angle.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: obtuse, B: obtuse, C: right, D: obtuse, E: obtuse, F: right
- Pick out the right angles. Count the corners that are a square corner.1 + 1 = 2
- Write the answer. Write how many corners are of this kind.2
Check. Right 2, acute 0 and obtuse 4 make 6 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: obtuse, B: obtuse, C: right, D: obtuse, E: obtuse, F: right
- Pick out the acute angles. Count the corners that are smaller than a square corner.0 corners of this kind
- Write the answer. Write how many corners are of this kind.0
Check. Right 2, acute 0 and obtuse 4 make 6 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a half turn.
Method. Compare each corner with a square corner, then count the corners of the kind asked for.
- Look at each corner in turn. Compare each corner with the corner of a square. A square corner is a right angle.A: obtuse, B: obtuse, C: right, D: obtuse, E: obtuse, F: right
- Pick out the obtuse angles. Count the corners that are bigger than a square corner.1 + 1 + 1 + 1 = 4
- Write the answer. Write how many corners are of this kind.4
Check. Right 2, acute 0 and obtuse 4 make 6 corners in all, the same as the number of sides. ✓
Watch out. A corner that looks nearly square can still be acute or obtuse. Check it against a square corner.
Key words. A horizontal line goes straight across. A vertical line goes straight up and down. Perpendicular lines meet at a right angle. Parallel lines never meet.
Method. Check the sides and the angles of a rectangle, one part at a time.
- Check the parallel sides. The opposite sides of a rectangle are parallel. There are two pairs.2 pairs of parallel sides
- Check the angles. Each corner of a rectangle is a square corner. A rectangle has 4 corners.4 right angles
- Write the answer. Ravi is right. A rectangle has two pairs of parallel sides and four right angles.Yes
Check. Each pair of opposite sides never meets, and every corner is a right angle. ✓
Watch out. Parallel sides go the same way and never meet. Right angles are square corners.