Year 4: Quadrilaterals and parallel lines
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Quadrilaterals and parallel lines
A quadrilateral is a shape with 4 straight sides and 4 corners. There are six special quadrilaterals to learn. To tell them apart we look at three things: the sides (which are equal?), the angles (any right angles?) and the parallel sides.
Parallel lines stay the same distance apart and never meet. We mark them with arrows (>). Perpendicular lines meet at a right angle.
Here are the six quadrilaterals and their properties. In this book a trapezium has exactly one pair of parallel sides.
| Shape | Name | Equal sides | Right angles | Pairs of parallel sides | Lines of symmetry |
|---|---|---|---|---|---|
| square | all 4 sides equal | 4 | 2 | 4 | |
| rectangle | opposite sides equal | 4 | 2 | 2 | |
| rhombus | all 4 sides equal | 0 | 2 | 2 | |
| parallelogram | opposite sides equal | 0 | 2 | 0 | |
| trapezium | no equal sides | 0 | 1 | 0 | |
| kite | two pairs of equal sides, next to each other | 0 | 0 | 1 |
Look carefully at the table. A square has everything: 4 equal sides, 4 right angles and 2 pairs of parallel sides. That means a square is a special kind of rectangle, and a special kind of rhombus. A rectangle has 4 right angles but only opposite sides are equal. A rhombus is like a leaning square: all sides equal but no right angles. A parallelogram is a leaning rectangle. A kite has two pairs of equal sides next to each other.
Key ideas
- A quadrilateral has 4 straight sides and 4 corners.
- Parallel sides never meet (arrows >). Perpendicular sides meet at a right angle (small square).
- Square: 4 equal sides, 4 right angles. Rectangle: 4 right angles, opposite sides equal. Rhombus: 4 equal sides, no right angles.
- Parallelogram: 2 pairs of parallel sides. Trapezium: 1 pair of parallel sides. Kite: 2 pairs of equal sides next to each other.
- A square is a special rectangle. Turning a shape does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has all 4 sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 0. - Decide on the name. All four sides are equal, but the angles are not right angles.It is a rhombus.
Check. The rhombus has all 4 sides equal, 2 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has opposite sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 4. - Decide on the name. Four right angles, and the sides are equal only in opposite pairs.It is a rectangle.
Check. The rectangle has opposite sides equal, 2 pair(s) of parallel sides and 4 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has no equal sides.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 1.
Right angles: 0. - Decide on the name. Exactly one pair of parallel sides.It is a trapezium.
Check. The trapezium has no equal sides, 1 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has two pairs of equal sides, next to each other.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 0.
Right angles: 0. - Decide on the name. Two pairs of equal sides next to each other, and no parallel sides.It is a kite.
Check. The kite has two pairs of equal sides, next to each other, 0 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Parallel sides stay the same distance apart and never meet. Arrow marks show sides that are parallel: sides with the same number of arrows are parallel to each other.
- Look at the arrow marks. Two sides with the same arrow marks are a pair of parallel sides.
- Write the sides with the same arrows. Use the letters at the two ends of each side.AB and CD; BC and DA
- Answer. The parallel sides are AB and CD; BC and DA.
Check. Pairs of parallel sides: 2. ✓
Watch out. Name each side with its two end letters, such as AB.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Perpendicular lines meet at a right angle. Look for the sides that meet PQ at a right angle.
- Look at the right angles. Small squares mark them.
- Find the sides that meet PQ at a right angle. These are the sides next to it.QR and SP
- Answer. QR and SP are perpendicular to PQ.
Check. Each of these meets PQ at a small square. ✓
Watch out. Sides opposite each other are parallel, not perpendicular.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. A square has all the properties of a rectangle: 4 right angles and opposite sides equal and parallel. It also has all sides equal.
- List what a rectangle needs. A rectangle has 4 right angles, and its opposite sides are equal and parallel.rectangle: 4 right angles; opposite sides equal and parallel
- Check the square. A square has 4 right angles, and its opposite sides are equal and parallel.square: 4 right angles; opposite sides equal and parallel ✓
- Answer. The square has everything a rectangle needs.Yes, a square is a rectangle. It is a special rectangle with all four sides equal.
Check. A square is a rectangle, but most rectangles are not squares. ✓
Watch out. Not every rectangle is a square.
Watch out
A shape keeps its name when it is turned. A square standing on one corner is still a square (do not call it a diamond). Also, a rhombus is not a square: it has four equal sides but its corners are not right angles. And do not forget: only pairs of sides are parallel. A trapezium has exactly one pair.Exercise 9D Quadrilaterals
Non-calculatorKey words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has all 4 sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 4. - Decide on the name. All sides are equal and all angles are right angles.It is a square.
Check. The square has all 4 sides equal, 2 pair(s) of parallel sides and 4 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has opposite sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 4. - Decide on the name. Four right angles, and the sides are equal only in opposite pairs.It is a rectangle.
Check. The rectangle has opposite sides equal, 2 pair(s) of parallel sides and 4 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has all 4 sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 0. - Decide on the name. All four sides are equal, but the angles are not right angles.It is a rhombus.
Check. The rhombus has all 4 sides equal, 2 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has opposite sides equal.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 2.
Right angles: 0. - Decide on the name. Two pairs of parallel sides, with no right angles and sides not all equal.It is a parallelogram.
Check. The parallelogram has opposite sides equal, 2 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has no equal sides.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 1.
Right angles: 0. - Decide on the name. Exactly one pair of parallel sides.It is a trapezium.
Check. The trapezium has no equal sides, 1 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Describe the shape: sides, then parallel sides, then right angles. Compare with the six quadrilaterals: square, rectangle, rhombus, parallelogram, trapezium and kite.
- Count the sides. A shape with 4 straight sides is a quadrilateral.It has 4 sides.
- Look at the sides. Tick marks show equal sides.The shape has two pairs of equal sides, next to each other.
- Look for parallel sides and right angles. Arrows on two sides mean they are parallel. A small square means a right angle.Pairs of parallel sides: 0.
Right angles: 0. - Decide on the name. Two pairs of equal sides next to each other, and no parallel sides.It is a kite.
Check. The kite has two pairs of equal sides, next to each other, 0 pair(s) of parallel sides and 0 right angle(s). ✓
Watch out. Turning a shape round does not change its name.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at each corner of the square. A small square marks a right angle. Count the squares.
- Draw the square. Right angles are marked with small squares.
- Count the right angles. Test each corner with the corner of a piece of paper.4 right angles.
- Write the answer. 4
Check. A square and a rectangle have 4; the others here have 0. ✓
Watch out. A rhombus is a leaning square, so it has no right angles.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at each corner of the rhombus. A small square marks a right angle. Count the squares.
- Draw the rhombus. Right angles are marked with small squares.
- Count the right angles. Test each corner with the corner of a piece of paper.0 right angles.
- Write the answer. 0
Check. A square and a rectangle have 4; the others here have 0. ✓
Watch out. A rhombus is a leaning square, so it has no right angles.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at each corner of the kite. A small square marks a right angle. Count the squares.
- Draw the kite. Right angles are marked with small squares.
- Count the right angles. Test each corner with the corner of a piece of paper.0 right angles.
- Write the answer. 0
Check. A square and a rectangle have 4; the others here have 0. ✓
Watch out. A rhombus is a leaning square, so it has no right angles.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at each corner of the rectangle. A small square marks a right angle. Count the squares.
- Draw the rectangle. Right angles are marked with small squares.
- Count the right angles. Test each corner with the corner of a piece of paper.4 right angles.
- Write the answer. 4
Check. A square and a rectangle have 4; the others here have 0. ✓
Watch out. A rhombus is a leaning square, so it has no right angles.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at the arrow marks on the square. Count the pairs of sides that are parallel.
- Draw the square. Arrows show parallel sides.
- Count the pairs. Each pair of parallel sides has the same arrows.2 pairs of parallel sides.
- Write the answer. 2
Check. A square has 2 pair(s) of parallel sides. ✓
Watch out. Pairs, not sides: two parallel sides make one pair.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at the arrow marks on the trapezium. Count the pairs of sides that are parallel.
- Draw the trapezium. Arrows show parallel sides.
- Count the pairs. Each pair of parallel sides has the same arrows.1 pair of parallel sides.
- Write the answer. 1
Check. A trapezium has 1 pair(s) of parallel sides. ✓
Watch out. Pairs, not sides: two parallel sides make one pair.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at the arrow marks on the kite. Count the pairs of sides that are parallel.
- Draw the kite. Arrows show parallel sides.
- Count the pairs. Each pair of parallel sides has the same arrows.0 pairs of parallel sides.
- Write the answer. 0
Check. A kite has 0 pair(s) of parallel sides. ✓
Watch out. Pairs, not sides: two parallel sides make one pair.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look at the arrow marks on the parallelogram. Count the pairs of sides that are parallel.
- Draw the parallelogram. Arrows show parallel sides.
- Count the pairs. Each pair of parallel sides has the same arrows.2 pairs of parallel sides.
- Write the answer. 2
Check. A parallelogram has 2 pair(s) of parallel sides. ✓
Watch out. Pairs, not sides: two parallel sides make one pair.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Parallel sides stay the same distance apart and never meet. Arrow marks show sides that are parallel: sides with the same number of arrows are parallel to each other.
- Look at the arrow marks. Two sides with the same arrow marks are a pair of parallel sides.
- Write the sides with the same arrows. Use the letters at the two ends of each side.AB and CD; BC and DA
- Answer. The parallel sides are AB and CD; BC and DA.
Check. Pairs of parallel sides: 2. ✓
Watch out. Name each side with its two end letters, such as AB.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Perpendicular lines meet at a right angle. Look for the sides that meet PQ at a right angle.
- Look at the right angles. Small squares mark them.
- Find the sides that meet PQ at a right angle. These are the sides next to it.QR and SP
- Answer. QR and SP are perpendicular to PQ.
Check. Each of these meets PQ at a small square. ✓
Watch out. Sides opposite each other are parallel, not perpendicular.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.
- Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
Nothing is crossed out. - Use the clue: “All of my sides are the same length.” Cross out every shape that does not fit. Keep the ones that do.Keep: square and rhombus.
Cross out: rectangle, parallelogram, trapezium and kite. - Use the clue: “I have four right angles.” Cross out every shape that does not fit. Keep the ones that do.Keep: square.
Cross out: rhombus. - Write the answer. Only one shape fits every clue.The shape is the square.
Check. Look at the square: every clue is true for it. ✓
Watch out. Read every clue. One clue on its own often fits more than one shape.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.
- Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
Nothing is crossed out. - Use the clue: “My opposite sides are equal in length.” Cross out every shape that does not fit. Keep the ones that do.Keep: square, rectangle, rhombus and parallelogram.
Cross out: trapezium and kite. - Use the clue: “I have four right angles.” Cross out every shape that does not fit. Keep the ones that do.Keep: square and rectangle.
Cross out: rhombus and parallelogram. - Use the clue: “My sides are not all the same length.” Cross out every shape that does not fit. Keep the ones that do.Keep: rectangle.
Cross out: square. - Write the answer. Only one shape fits every clue.The shape is the rectangle.
Check. Look at the rectangle: every clue is true for it. ✓
Watch out. Read every clue. One clue on its own often fits more than one shape.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Use the clues one at a time. After each clue, cross out the shapes that cannot be the answer. The shape that is left is the answer.
- Use the clue: “I have 4 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: square, rectangle, rhombus, parallelogram, trapezium and kite.
Nothing is crossed out. - Use the clue: “I have exactly one pair of parallel sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: trapezium.
Cross out: square, rectangle, rhombus, parallelogram and kite. - Write the answer. Only one shape fits every clue.The shape is the trapezium.
Check. Look at the trapezium: every clue is true for it. ✓
Watch out. Read every clue. One clue on its own often fits more than one shape.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check the statement against what you know about the shape.
- Think about the shape. Use the properties of the shape.A rectangle has 4 right angles (see the table).
- Decide. Is the statement true or false?The statement is true.
Check. Look at the table of shapes to be sure. ✓
Watch out. Check every part of the sentence.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check the statement against what you know about the shape.
- Think about the shape. Use the properties of the shape.A rhombus has four equal sides but no right angles. It leans over.
- Decide. Is the statement true or false?The statement is false.
Check. Look at the table of shapes to be sure. ✓
Watch out. Check every part of the sentence.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check the statement against what you know about the shape.
- Think about the shape. Use the properties of the shape.A kite has two pairs of equal sides next to each other.
- Decide. Is the statement true or false?The statement is true.
Check. Look at the table of shapes to be sure. ✓
Watch out. Check every part of the sentence.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check the statement against what you know about the shape.
- Think about the shape. Use the properties of the shape.A trapezium has exactly one pair of parallel sides.
- Decide. Is the statement true or false?The statement is false.
Check. Look at the table of shapes to be sure. ✓
Watch out. Check every part of the sentence.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. A square has four equal sides and four right angles. Check the shape for both.
- Look at the sides. Tick marks show the sides are all equal.All four sides are equal. That fits a square.
- Look at the angles. A square needs 4 right angles. There are no small squares on this shape.There are no right angles. This does not fit a square.
- Name the shape. Four equal sides and no right angles is a rhombus.No, Priya is wrong. It is a rhombus.
Check. The shape leans over, so the corners are not square. ✓
Watch out. A square needs right angles as well as equal sides.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Look for the shape with two pairs of equal sides that are next to each other. The tick marks show the equal sides.
- Look at the tick marks on each shape. The same number of ticks means equal sides.ABCD
- Describe the equal sides. Check whether the equal sides are opposite or next to each other.A: opposite sides equal
B: two pairs of equal sides, next to each other
C: opposite sides equal
D: no equal sides - Choose. Shape B has two pairs of equal sides next to each other. It is a kite.
Check. A kite is the shape of a flying kite. ✓
Watch out. In a parallelogram the equal sides are opposite, not next to each other.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Draw the rectangle and the cut. Look at the two triangles. Find the right angle and the sides of one triangle.
- Draw the cut. The cut goes from one corner to the opposite corner.
- Look at the corner of the whole shape. Every corner of a rectangle is a right angle. A corner is also a corner of each triangle.Each triangle has a right angle.
- Look at the sides. Check whether two sides of the triangle are equal.The two sides next to the right angle are 4 cm and 3 cm. They are different lengths.
- Name the triangle. Each triangle is a right-angled triangle.
Check. Two of these triangles fit together to make the rectangle. ✓
Watch out. The right angle of the rectangle stays in the triangle.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Draw the square and the cut. Look at the two triangles. Find the right angle and the sides of one triangle.
- Draw the cut. The cut goes from one corner to the opposite corner.
- Look at the corner of the whole shape. Every corner of a square is a right angle. A corner is also a corner of each triangle.Each triangle has a right angle.
- Look at the sides. Check whether two sides of the triangle are equal.The two sides next to the right angle are equal, because a square has equal sides.
- Name the triangle. Each triangle is a right-angled isosceles triangle.
Check. Two of these triangles fit together to make the square. ✓
Watch out. The right angle of the rectangle stays in the triangle.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. A square has 4 right angles and opposite sides equal and parallel. That is what a rectangle needs.
- List what a rectangle needs. 4 right angles, opposite sides equal.Rectangle: 4 right angles; opposite sides equal.
- Check a square. It has 4 right angles, and its opposite sides are equal.A square has all of these.
- Decide. This is always true.
Check. Every square is a rectangle. ✓
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Some rectangles have four equal sides and some do not. Try one of each.
- Try a 3 by 3 rectangle. All four sides are 3.This rectangle is a square.
- Try a 5 by 3 rectangle. The sides are 5, 3, 5, 3.This rectangle is not a square.
- Decide. This is sometimes true.
Check. We found a rectangle that is a square, and one that is not. ✓
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. A rhombus has four equal sides. Its angles can be square or leaning.
- Try a leaning rhombus. Like the one in the table.It has no right angles.
- Try a rhombus that stands straight. This is a square.It has four right angles.
- Decide. This is sometimes true.
Check. Only the square is a rhombus with right angles. ✓
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. A trapezium has exactly one pair of parallel sides in this book.
- Remember the meaning. Exactly one pair.A trapezium has 1 pair of parallel sides.
- Compare. Two pairs would make it a parallelogram.It cannot have two pairs.
- Decide. This is never true.
Check. A shape with two pairs of parallel sides is a parallelogram (or a rectangle, square or rhombus). ✓
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Find something that three of the shapes share. The odd one out is the shape that does not have it.
- Look at the parallel sides. Arrows show parallel sides.ABCD
- Count the pairs of parallel sides. A: 2 pairs
B: 2 pairs
C: 2 pairs
D: 0 pairs - Find the odd one out. Three shapes have two pairs of parallel sides.Shape D (the kite) has no parallel sides.
Check. A kite has no parallel sides but the other three shapes have two pairs. ✓
Watch out. There can be more than one reason. Any correct reason is fine.