Year 4: Polygons and sorting shapes
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Polygons and sorting shapes
A polygon is a flat shape that has straight sides and is closed (no gaps). A circle is not a polygon because it has a curved edge. The corners of a polygon are called vertices (one corner is a vertex). A polygon always has the same number of vertices as sides. We name a polygon by the number of its sides.
Regular and irregular. A polygon is regular if all its sides are equal and all its angles are equal. If not, it is irregular. A square is a regular quadrilateral. A rectangle is irregular, because its sides are not all equal. A rhombus is irregular too, because its angles are not all equal.
Sorting shapes. We can sort shapes using a Carroll diagram (a table with yes and no) or a Venn diagram (circles). In a Venn diagram, a shape that fits both labels goes in the part where the circles overlap. A shape that fits neither goes outside the circles, but inside the box.
| has a right angle | no right angle | |
|---|---|---|
| 4 sides | A, B | C, D |
| not 4 sides | E | F |
Key ideas
- A polygon is a closed flat shape with straight sides. A vertex is a corner. Sides and vertices are the same number.
- Names: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.
- Regular: all sides equal and all angles equal. Otherwise irregular.
- Carroll diagram: a table with yes and no. Venn diagram: a shape with both labels goes in the overlap.
- To solve “Which shape am I?”, use one clue at a time and cross out the shapes that do not fit.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 7 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 7 in the list.7 sides: heptagon
Check. The shape has 7 corners as well as 7 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 5 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 5 in the list.5 sides: pentagon
- Is it regular? Regular means all sides equal and all angles equal.Yes, so it is a regular pentagon.
Check. The shape has 5 corners as well as 5 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal and all its angles equal. Check both.
- Look at the sides. Tick marks show equal sides. Regular needs all sides equal.All the sides are equal.
- Look at the angles. Regular also needs all the angles equal. The orange arcs show the angles.The angles are not all equal.
- Decide. A regular polygon has equal sides and equal angles.This polygon is irregular.
Check. Regular needs both: sides equal, angles not equal. ✓
Watch out. Equal sides are not enough: a rhombus has four equal sides but it is not regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is a closed flat shape with only straight sides. Check each shape for two things: no gaps, and no curved sides.
- Remember what a polygon needs. It must be closed and have only straight sides.closed + straight sides = polygon
- Check each shape for gaps and curves. Look at every shape in turn.A: a closed shape with straight sides: a polygon.
B: It has a curved edge and no straight sides, so it is not a polygon.
C: It is not closed. There is a gap, so it is not a polygon.
D: a closed shape with straight sides: a polygon. - Pick the polygons. The polygons are A and D.
Check. Every polygon you picked is closed and has straight sides only. ✓
Watch out. A circle is not a polygon.
| has a right angle | no right angle | |
|---|---|---|
| 4 sides | ||
| not 4 sides |
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test every shape against both labels. Then put it in the box that matches the answers: yes or no for each label.
- Look at each shape. Ask the two questions about each shape.A: yes for “has 4 sides”, yes for “has a right angle”
B: yes for “has 4 sides”, yes for “has a right angle”
C: yes for “has 4 sides”, no for “has a right angle”
D: yes for “has 4 sides”, no for “has a right angle”
E: no for “has 4 sides”, yes for “has a right angle”
F: no for “has 4 sides”, no for “has a right angle” - Fill in the Carroll diagram. Each shape goes in exactly one box.
has a right angle not: has a right angle has 4 sides A, B C, D not: has 4 sides E F - Check. Count the shapes.6 shapes are in the diagram. There are 6 shapes. They all fit.
Check. Every shape is in exactly one box. ✓
Watch out. Every shape belongs in a box, even if it does not have either property.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test each shape against both labels. Both yes: the middle where the circles overlap. Only the left label: the left circle only. Only the right label: the right circle only. Neither: outside the circles.
- Test each shape. Ask the two questions about each shape.A: “has parallel sides” yes, “all sides equal” no
B: “has parallel sides” yes, “all sides equal” yes
C: “has parallel sides” no, “all sides equal” no
D: “has parallel sides” no, “all sides equal” yes
E: “has parallel sides” yes, “all sides equal” no
F: “has parallel sides” no, “all sides equal” no - Put the shapes in the Venn diagram. Shapes that fit both labels go in the overlap.
- Write the answer. Only “has parallel sides”: A and E. Both: B. Only “all sides equal”: D. Neither: C and F.
Check. 2 + 1 + 1 + 2 = 6 shapes. ✓
Watch out. Shapes with neither property go outside the circles but inside the box.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “I have two pairs of parallel sides.” 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 no right angles.” Cross out every shape that does not fit. Keep the ones that do.Keep: rhombus and parallelogram.
Cross out: square and rectangle. - 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: rhombus.
Cross out: parallelogram. - Write the answer. Only one shape fits every clue.The shape is the rhombus.
Check. Look at the rhombus: every clue is true for it. ✓
Watch out. Read every clue. One clue on its own often fits more than one shape.
Watch out
Equal sides are not enough for a regular polygon. A rhombus has four equal sides, but it is not regular because its angles are not all equal. A regular polygon needs equal sides and equal angles. Also, when you sort shapes, do not forget the shapes that fit neither label: they still go in the diagram.Exercise 9E Polygons
Non-calculatorKey words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 5 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 5 in the list.5 sides: pentagon
Check. The shape has 5 corners as well as 5 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 6 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 6 in the list.6 sides: hexagon
Check. The shape has 6 corners as well as 6 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 8 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 8 in the list.8 sides: octagon
Check. The shape has 8 corners as well as 8 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is named by its number of sides. Count the sides (or the corners, which are the same number) and use the name for that number.
- Count the sides. Number each corner as you count round the shape. The last number is the number of sides.The shape has 7 sides.
- Remember the names of the polygons. The name depends on the number of sides.triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10
- Find the name. Look for 7 in the list.7 sides: heptagon
Check. The shape has 7 corners as well as 7 sides. ✓
Watch out. Count carefully. Number each side so you do not count one twice.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A hexagon is the polygon with 6 sides. A polygon has the same number of corners (vertices) as sides.
- Find the number of sides in a hexagon. Remember the names: pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.hexagon = 6 sides
- Find the number of vertices. Each side joins two corners, so there are as many corners as sides.6 vertices
- Write the answer. 6 sides and 6 vertices
Check. Draw a hexagon and count: 6 sides and 6 corners. ✓
Watch out. Vertices are corners. There is one for each side.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A octagon is the polygon with 8 sides. A polygon has the same number of corners (vertices) as sides.
- Find the number of sides in a octagon. Remember the names: pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.octagon = 8 sides
- Find the number of vertices. Each side joins two corners, so there are as many corners as sides.8 vertices
- Write the answer. 8 sides and 8 vertices
Check. Draw a octagon and count: 8 sides and 8 corners. ✓
Watch out. Vertices are corners. There is one for each side.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A pentagon is the polygon with 5 sides. A polygon has the same number of corners (vertices) as sides.
- Find the number of sides in a pentagon. Remember the names: pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.pentagon = 5 sides
- Find the number of vertices. Each side joins two corners, so there are as many corners as sides.5 vertices
- Write the answer. 5 sides and 5 vertices
Check. Draw a pentagon and count: 5 sides and 5 corners. ✓
Watch out. Vertices are corners. There is one for each side.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A decagon is the polygon with 10 sides. A polygon has the same number of corners (vertices) as sides.
- Find the number of sides in a decagon. Remember the names: pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.decagon = 10 sides
- Find the number of vertices. Each side joins two corners, so there are as many corners as sides.10 vertices
- Write the answer. 10 sides and 10 vertices
Check. Draw a decagon and count: 10 sides and 10 corners. ✓
Watch out. Vertices are corners. There is one for each side.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Match the number of sides to the name of the polygon.
- Remember the names. Triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.tri = 3, quad = 4, penta = 5, hexa = 6, hepta = 7, octa = 8, nona = 9, deca = 10
- Find 7. 7 sides is a heptagon.
Check. A heptagon has 7 sides. ✓
Watch out. Octa means 8 (like an octopus with 8 legs).
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Match the number of sides to the name of the polygon.
- Remember the names. Triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.tri = 3, quad = 4, penta = 5, hexa = 6, hepta = 7, octa = 8, nona = 9, deca = 10
- Find 9. 9 sides is a nonagon.
Check. A nonagon has 9 sides. ✓
Watch out. Octa means 8 (like an octopus with 8 legs).
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Match the number of sides to the name of the polygon.
- Remember the names. Triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.tri = 3, quad = 4, penta = 5, hexa = 6, hepta = 7, octa = 8, nona = 9, deca = 10
- Find 6. 6 sides is a hexagon.
Check. A hexagon has 6 sides. ✓
Watch out. Octa means 8 (like an octopus with 8 legs).
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Match the number of sides to the name of the polygon.
- Remember the names. Triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.tri = 3, quad = 4, penta = 5, hexa = 6, hepta = 7, octa = 8, nona = 9, deca = 10
- Find 4. 4 sides is a quadrilateral.
Check. A quadrilateral has 4 sides. ✓
Watch out. Octa means 8 (like an octopus with 8 legs).
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A polygon is a closed flat shape with only straight sides. Check each shape for two things: no gaps, and no curved sides.
- Remember what a polygon needs. It must be closed and have only straight sides.closed + straight sides = polygon
- Check each shape for gaps and curves. Look at every shape in turn.A: a closed shape with straight sides: a polygon.
B: It has a curved edge and no straight sides, so it is not a polygon.
C: It is not closed. There is a gap, so it is not a polygon.
D: a closed shape with straight sides: a polygon.
E: It has a curved edge, so it is not a polygon.
F: a closed shape with straight sides: a polygon. - Pick the polygons. The polygons are A, D and F.
Check. Every polygon you picked is closed and has straight sides only. ✓
Watch out. A circle is not a polygon.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal and all its angles equal. Check both.
- Look at the sides. Tick marks show equal sides. Regular needs all sides equal.All the sides are equal.
- Look at the angles. Regular also needs all the angles equal. The orange arcs show the angles.All the angles are equal.
- Decide. A regular polygon has equal sides and equal angles.This is a regular polygon.
Check. Regular needs both: sides equal, angles equal. ✓
Watch out. Equal sides are not enough: a rhombus has four equal sides but it is not regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal and all its angles equal. Check both.
- Look at the sides. Tick marks show equal sides. Regular needs all sides equal.The sides are not all equal.
- Look at the angles. Regular also needs all the angles equal. The orange arcs show the angles.All the angles are equal.
- Decide. A regular polygon has equal sides and equal angles.This polygon is irregular.
Check. Regular needs both: sides not equal, angles equal. ✓
Watch out. Equal sides are not enough: a rhombus has four equal sides but it is not regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal and all its angles equal. Check both.
- Look at the sides. Tick marks show equal sides. Regular needs all sides equal.All the sides are equal.
- Look at the angles. Regular also needs all the angles equal. The orange arcs show the angles.The angles are not all equal.
- Decide. A regular polygon has equal sides and equal angles.This polygon is irregular.
Check. Regular needs both: sides equal, angles not equal. ✓
Watch out. Equal sides are not enough: a rhombus has four equal sides but it is not regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal and all its angles equal. Check both.
- Look at the sides. Tick marks show equal sides. Regular needs all sides equal.The sides are not all equal.
- Look at the angles. Regular also needs all the angles equal. The orange arcs show the angles.The angles are not all equal.
- Decide. A regular polygon has equal sides and equal angles.This polygon is irregular.
Check. Regular needs both: sides not equal, angles not equal. ✓
Watch out. Equal sides are not enough: a rhombus has four equal sides but it is not regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all sides equal. So the number of equal sides is the same as the number of sides. A polygon has as many vertices as sides.
- Find the number of sides. Octa means 8. Hexa means 6.octagon: 8 sides; hexagon: 6 sides
- Write the numbers. Equal sides: all of them. Vertices: one for each side.regular octagon: 8 equal sides; regular hexagon: 6 vertices
Check. Draw them and count. ✓
Watch out. Regular means every side is the same, so you count all of them.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all sides equal. So the number of equal sides is the same as the number of sides. A polygon has as many vertices as sides.
- Find the number of sides. Octa means 8. Hexa means 6.octagon: 8 sides; hexagon: 6 sides
- Write the numbers. Equal sides: all of them. Vertices: one for each side.regular octagon: 8 equal sides; regular hexagon: 6 vertices
Check. Draw them and count. ✓
Watch out. Regular means every side is the same, so you count all of them.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A stop sign is a regular octagon. A regular octagon has 8 equal sides. The perimeter is the distance all the way round, so add all 8 sides, or multiply.
- Find the number of sides. Octagon means 8 sides.8 sides
- Multiply to find the perimeter. 8 equal sides of 25 cm each.8 × 25 = 200
- Write the answer with the unit. 200 cm (that is 2 m)
Check. 25 + 25 + 25 + 25 + 25 + 25 + 25 + 25 = 200. ✓
Watch out. Do not forget the units.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A hexagon has 6 sides. Mei draws 5 hexagons, so find 5 groups of 6.
- Find the sides in one hexagon. Hexa means 6.6 sides
- Multiply by 5. 5 hexagons with 6 sides each.5 × 6 = 30
- Write the answer. Mei draws 30 sides altogether.
Check. 6 + 6 + 6 + 6 + 6 = 30. ✓
Watch out. Count the sides of all the hexagons.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Regular needs equal sides and equal angles. Check the angles as well as the sides.
- Look at what Noah says. He says all six sides are equal, so the hexagon is regular.Noah: “6 equal sides, so it is regular.”
- Check the sides. The tick marks show that all six sides are equal.Noah is right about the sides.
- Check the angles. A regular polygon has equal angles. Two of the angles in this hexagon are narrower than the other four.The angles are not all equal.
- Answer. No, Noah is wrong. The hexagon has equal sides, but its angles are not equal, so it is irregular.
Check. Compare with a regular hexagon: all six corners look the same. This one does not. ✓
Watch out. Check both sides and angles.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A rectangle has 4 right angles, so its angles are equal. But its sides are not all equal.
- Check the sides. A rectangle that is not a square has sides of two different lengths.sides: 5, 3, 5, 3
- Check the angles. All four are right angles.angles all equal
- Decide. A regular polygon needs equal sides too.The statement is false.
Check. A square would be regular, but a rectangle is not always a square. ✓
Watch out. Both sides and angles must be equal.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A square has 4 equal sides and 4 equal angles (right angles).
- Check the sides. A square has four equal sides.sides: 3, 3, 3, 3
- Check the angles. All four are right angles.angles all equal
- Decide. Both are equal.The statement is true.
Check. A square is a regular quadrilateral. ✓
Watch out. A square is regular.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A triangle is a closed shape with 3 straight sides.
- Remember what a polygon is. A closed flat shape with straight sides.closed, straight sides
- Check a triangle. It has 3 straight sides and no gaps.It fits.
- Decide. The statement is true.
Check. A triangle is the polygon with the fewest sides. ✓
Watch out. The smallest polygon is a triangle.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has equal sides. The perimeter is the sum of all sides, so the number of sides is the perimeter divided by the length of one side.
- Write what we know. Each side is 4 cm and the perimeter is 32 cm.perimeter ÷ one side = number of sides
- Divide. How many 4 cm sides make 32 cm?32 ÷ 4 = 8
- Name the polygon. A polygon with 8 sides is an octagon.It is a regular octagon.
Check. 8 × 4 = 32. ✓
Watch out. Remember to name the polygon, not just give the number.
Exercise 9F Sorting shapes
Non-calculator| has a right angle | no right angle | |
|---|---|---|
| 4 sides | ||
| not 4 sides |
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test every shape against both labels. Then put it in the box that matches the answers: yes or no for each label.
- Look at each shape. Ask the two questions about each shape.A: yes for “has 4 sides”, yes for “has a right angle”
B: yes for “has 4 sides”, yes for “has a right angle”
C: no for “has 4 sides”, yes for “has a right angle”
D: no for “has 4 sides”, no for “has a right angle”
E: yes for “has 4 sides”, no for “has a right angle”
F: yes for “has 4 sides”, no for “has a right angle”
G: no for “has 4 sides”, yes for “has a right angle”
H: no for “has 4 sides”, no for “has a right angle” - Fill in the Carroll diagram. Each shape goes in exactly one box.
has a right angle not: has a right angle has 4 sides A, B E, F not: has 4 sides C, G D, H - Check. Count the shapes.8 shapes are in the diagram. There are 8 shapes. They all fit.
Check. Every shape is in exactly one box. ✓
Watch out. Every shape belongs in a box, even if it does not have either property.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test each shape against both labels. Both yes: the middle where the circles overlap. Only the left label: the left circle only. Only the right label: the right circle only. Neither: outside the circles.
- Test each shape. Ask the two questions about each shape.A: “has parallel sides” yes, “all sides equal” no
B: “has parallel sides” yes, “all sides equal” yes
C: “has parallel sides” no, “all sides equal” no
D: “has parallel sides” no, “all sides equal” yes
E: “has parallel sides” yes, “all sides equal” no
F: “has parallel sides” no, “all sides equal” no - Put the shapes in the Venn diagram. Shapes that fit both labels go in the overlap.
- Write the answer. Only “has parallel sides”: A and E. Both: B. Only “all sides equal”: D. Neither: C and F.
Check. 2 + 1 + 1 + 2 = 6 shapes. ✓
Watch out. Shapes with neither property go outside the circles but inside the box.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. The right circle holds the shapes that have the missing property. Find what the shapes in the right circle all have, and what the other shapes do not have.
- Look at the shapes in the right circle. These shapes are in the right circle: A, B and E.ABCDEF
- Find what they share. Check their sides, angles and parallel sides.The square, equilateral triangle and regular hexagon all have all sides equal. (They are also all regular, so “is regular” is a good label too.)
- Check the shapes that are not in the right circle. They should not have this property.The kite, parallelogram and right-angled triangle do not have all sides equal. So the label fits.
Check. No shape outside the right circle has all sides equal. ✓
Watch out. Check the shapes that are not in the circle too.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test the shape against both labels, then choose the part of the Venn diagram.
- Test the rhombus for the left label. The left label is “has parallel sides”.Yes.
- Test the rhombus for the right label. The right label is “all sides equal”.Yes.
- Choose the region. Both yes: overlap. One yes: that circle only. Both no: outside.The rhombus goes in the overlap (both circles).
Check. The rhombus is “has parallel sides” and “all sides equal”. ✓
Watch out. A shape that has neither property goes outside the circles.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test the shape against both labels, then choose the part of the Venn diagram.
- Test the kite for the left label. The left label is “has parallel sides”.No.
- Test the kite for the right label. The right label is “all sides equal”.No.
- Choose the region. Both yes: overlap. One yes: that circle only. Both no: outside.The kite goes outside both circles.
Check. The kite is not “has parallel sides” and not “all sides equal”. ✓
Watch out. A shape that has neither property goes outside the circles.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Test the shape against both labels, then choose the part of the Venn diagram.
- Test the rectangle for the left label. The left label is “has parallel sides”.Yes.
- Test the rectangle for the right label. The right label is “all sides equal”.No.
- Choose the region. Both yes: overlap. One yes: that circle only. Both no: outside.The rectangle goes in the left circle only.
Check. The rectangle is “has parallel sides” and not “all sides equal”. ✓
Watch out. A shape that has neither property goes outside the circles.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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 3 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: equilateral triangle, isosceles triangle, scalene triangle and right-angled triangle.
Cross out: square, rectangle, rhombus, parallelogram, trapezium, kite, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - 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: equilateral triangle.
Cross out: isosceles triangle, scalene triangle and right-angled triangle. - Write the answer. Only one shape fits every clue.The shape is the equilateral triangle.
Check. Look at the equilateral triangle: 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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 6 sides.” Cross out every shape that does not fit. Keep the ones that do.Keep: regular hexagon.
Cross out: square, rectangle, rhombus, parallelogram, trapezium, kite, equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “I am a regular polygon.” Cross out every shape that does not fit. Keep the ones that do.Keep: regular hexagon.
Nothing is crossed out. - Write the answer. Only one shape fits every clue.The shape is the regular hexagon.
Check. Look at the regular hexagon: 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “I have four lines of symmetry.” Cross out every shape that does not fit. Keep the ones that do.Keep: square.
Cross out: rectangle, rhombus, parallelogram, trapezium and kite. - 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “I have two pairs of equal sides, and the equal sides are next to each other.” Cross out every shape that does not fit. Keep the ones that do.Keep: kite.
Cross out: square, rectangle, rhombus, parallelogram and trapezium. - Write the answer. Only one shape fits every clue.The shape is the kite.
Check. Look at the kite: 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - 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. - Use the clue: “I have no right angles.” Cross out every shape that does not fit. Keep the ones that do.Keep: trapezium.
Nothing is crossed out. - 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
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.
Cross out: equilateral triangle, isosceles triangle, scalene triangle, right-angled triangle, regular pentagon, regular hexagon, regular heptagon, regular octagon, regular nonagon and regular decagon. - Use the clue: “I have two pairs of parallel sides.” 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: “Two of my angles are acute and two are obtuse.” Cross out every shape that does not fit. Keep the ones that do.Keep: rhombus and parallelogram.
Cross out: square and rectangle. - 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: parallelogram.
Cross out: rhombus. - Use the clue: “I have no right angles.” Cross out every shape that does not fit. Keep the ones that do.Keep: parallelogram.
Nothing is crossed out. - Write the answer. Only one shape fits every clue.The shape is the parallelogram.
Check. Look at the parallelogram: 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 Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Look for a property that three shapes share. Test the property “has a right angle” on every shape.
- Test every shape. Does the shape fit “has a right angle”?ABCDA (rectangle): yes
B (square): yes
C (right-angled triangle): yes
D (parallelogram): no - Find the odd one out. Three say yes. One says no.Shape D (parallelogram) is the odd one out.
Check. Only D gives a different answer. ✓
Watch out. There may be another correct reason. Any true reason is fine.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Look for a property that three shapes share. Test the property “is regular” on every shape.
- Test every shape. Does the shape fit “is regular”?ABCDA (equilateral triangle): yes
B (regular hexagon): yes
C (square): yes
D (kite): no - Find the odd one out. Three say yes. One says no.Shape D (kite) is the odd one out.
Check. Only D gives a different answer. ✓
Watch out. There may be another correct reason. Any true reason is fine.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Look for a property that three shapes share. Test the property “has two pairs of parallel sides” on every shape.
- Test every shape. Does the shape fit “has two pairs of parallel sides”?ABCDA (rhombus): yes
B (parallelogram): yes
C (trapezium): no
D (rectangle): yes - Find the odd one out. Three say yes. One says no.Shape C (trapezium) is the odd one out.
Check. Only C gives a different answer. ✓
Watch out. There may be another correct reason. Any true reason is fine.
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A regular polygon has all its sides equal. That is part of the meaning of regular.
- Remember the meaning. Regular means equal sides and equal angles.regular = equal sides + equal angles
- Check. So a regular polygon always has equal sides.True for every regular polygon.
- Decide. This is always true.
Check. A regular hexagon, a square and a regular triangle all have equal sides. ✓
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Some pentagons are regular and some are not. Try both.
- Try a regular pentagon. All sides and angles are equal.It is regular.
- Try an irregular pentagon. Like the house shape.It is not regular.
- Decide. This is sometimes true.
Check. We found a pentagon that is regular and one that is not. ✓
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. Hexa means 6. A hexagon has 6 sides.
- Remember the name. Hexagon = 6 sides.hexagon: 6 sides
- Compare. The sentence says 7.6 is not 7.
- Decide. This is never true.
Check. A heptagon has 7 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. A square has four right angles. A kite or a rhombus does not.
- Try a square or rectangle. These have four right angles.The statement is true.
- Try a rhombus. This has no right angles.The statement is not true.
- Decide. This is sometimes true.
Check. We found a quadrilateral with four right angles and one without. ✓
Key words. A polygon is a flat shape with straight sides that is closed (no gaps). A vertex is a corner (the plural is vertices). A regular polygon has equal sides and equal angles. An irregular polygon does not.
Method. A quadrilateral has 4 sides. Count the sides of each shape, then count the shapes that have 4.
- Count the sides of each shape. Count carefully.A: 4 sides
B: 4 sides
C: 3 sides
D: 3 sides
E: 4 sides
F: 4 sides
G: 5 sides
H: 6 sides - Pick the shapes with 4 sides. A, B, E and F
- Count them. There are 4 quadrilaterals.
Check. 4 shapes have 4 sides. ✓
Watch out. A quadrilateral is any shape with exactly 4 sides.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. Check each shape against both labels. Find the shape that is in the wrong part of the diagram.
- Test the shapes. Left label: has parallel sides. Right label: all sides equal.ABCDEF
- Find the shape in the wrong place. Shape B has parallel sides and all sides equal (it is a rhombus), so it belongs in the overlap, but it is outside the circles.The mistake is shape B.
- Say where it should go. Shape B should go in the overlap.
Check. All the other shapes are in the right place. ✓
Watch out. Check every shape, one at a time.
Key words. A Venn diagram uses circles. Things that fit both labels go in the part where the circles overlap. A Carroll diagram is a table with yes and no.
Method. A shape in the middle must have both properties: 4 sides and a right angle. Check each four-sided shape for a right angle.
- List the shapes with 4 sides. These are the quadrilaterals.square, rectangle, rhombus, parallelogram, trapezium, kite
- Check each one for a right angle. Look at the corners.square: has right angles
rectangle: has right angles
rhombus: no right angle
parallelogram: no right angle
trapezium: no right angle
kite: no right angle - Answer. The shapes that have both.square and rectangle can go in the middle.
Check. A rhombus, parallelogram or kite could not go there. ✓
Watch out. Check each shape for both labels.