Year 6 Maths: Similar Shapes

What Are Similar Shapes?

Hello Year 6! Today, we’re going to learn about similar shapes. Similar shapes are shapes that look alike but can be different sizes. They have the same shape but do not have to be the same size.

Key Rules of Similar Shapes

1. Same Shape: Similar shapes have the same angles. This means if you measured all the angles in one shape, they would match the angles in the other shape.
2. Different Sizes: The sizes can be different. One shape might be bigger or smaller than the other.
3. Proportional Sides: The lengths of the sides are in proportion. This means if you compare the lengths of the sides, the ratios (the relationship between the sizes) will be the same.For example, if one triangle has sides of 2 cm, 3 cm, and 4 cm, a similar triangle might have sides of 4 cm, 6 cm, and 8 cm. The ratios are the same!

Examples

• Example 1: Think of a small drawing of a square and a larger square. They are similar because they have the same angles (90 degrees) and the sides are in proportion.
• Example 2: Consider two triangles. If one triangle has angles of 30°, 60°, and 90°, and the other triangle also has the same angles, they are similar, regardless of their side lengths.

Tips and Tricks

• Check Angles: Always check the angles first! If the angles are the same, the shapes are similar.
• Compare Sides: Measure the sides. If the sides are in proportion, the shapes are similar.
• Use Ratios: You can write the ratios of the sides. For example, if one shape has sides of 3 cm and 6 cm, and the other shape has sides of 1.5 cm and 3 cm, you can see that the ratios are the same: $$\frac{3}{1.5} = 2$$ and $$\frac{6}{3} = 2$$

Practice Questions

Easy Level Questions

1. Are two squares with different sizes similar shapes? (Yes/No)
2. If one triangle has angles 30°, 60°, and 90°, and another triangle has angles 30°, 60°, and 90°, are they similar? (Yes/No)
3. True or False: Similar shapes must have the same area.
4. What is the ratio of the sides of a triangle with sides 2 cm, 4 cm, and a similar triangle with sides 4 cm, 8 cm? (1:2)
5. Name two similar shapes.
6. How many degrees are in a right angle? (90)
7. If a rectangle has sides 2 cm and 4 cm, and a similar rectangle has sides 4 cm and 8 cm, are they similar? (Yes/No)
8. True or False: All circles are similar shapes.
9. What shape remains similar when enlarged? (Circle)
10. Are two rectangles with angles of 90° similar if one is larger? (Yes/No)

Medium Level Questions

11. Triangle A has sides 3 cm, 4 cm, and 5 cm. Triangle B has sides 6 cm, 8 cm, and 10 cm. Are they similar? (Yes/No)
12. What is the scale factor between a triangle with sides 5 cm and a similar triangle with sides 10 cm? (2)
13. Identify: If two shapes have the same angles but different side lengths, what are they called? (Similar shapes)
14. If a shape’s width is doubled, what happens to its height for it to remain similar? (Must be doubled)
15. True or False: Two shapes can be similar if one is a reflection of the other.
16. What is the ratio of a shape with sides 10 cm and a similar shape with sides 5 cm? (2:1)
17. Can a triangle with angles 45°, 45°, and 90° be similar to a triangle with angles 60°, 60°, and 60°? (Yes/No)
18. If a rectangle has a length of 4 cm and a width of 2 cm, what are the dimensions of a similar rectangle with a length of 8 cm? (4 cm)
19. If two shapes have a similarity ratio of 1:3, how much bigger is the larger shape compared to the smaller shape? (3 times)
20. True or False: Similar shapes can be different colours.

Hard Level Questions

21. Triangle A has sides 6 cm, 8 cm, and 10 cm. Triangle B has a side of 9 cm. What is the length of the other two sides of Triangle B to keep it similar? (12 cm and 15 cm)
22. If a shape has a perimeter of 20 cm and a similar shape has a perimeter of 30 cm, what is the scale factor? (1.5)
23. A triangle has sides in the ratio of 2:3:4. If the smallest side is 6 cm, what are the lengths of the other two sides? (9 cm and 12 cm)
24. If two similar shapes have a scale factor of 3:5, and the smaller shape has a side of 12 cm, what is the corresponding side of the larger shape? (20 cm)
25. If two similar rectangles have a length ratio of 1:4, what is the ratio of their areas? (1:16)
26. Two circles have radii in the ratio of 1:2. What is the ratio of their areas? (1:4)
27. True or False: If a rectangle is similar to a square, the square must have equal sides.
28. If a triangle has angles of 70°, 60°, and 50°, what is the angle measure of the similar triangle? (Same angles)
29. A shape with a length of 5 cm is similar to a shape with a length of 15 cm. What is the scale factor? (3)
30. If a triangle’s sides are in the ratio of 3:4:5 and the smallest side is 9 cm, find the lengths of the other sides. (12 cm and 15 cm)

Answers and Explanations

Easy Level Answers

1. Yes
2. Yes
3. True
4. 1:2
5. Square and rectangle
6. 90
7. Yes
8. True
9. Circle
10. Yes

Medium Level Answers

11. Yes
12. 2
13. Similar shapes
14. Must be doubled
15. True
16. 2:1
17. No
18. 4 cm
19. 3 times
20. True

Hard Level Answers

21. 12 cm and 15 cm
22. 1.5
23. 9 cm and 12 cm
24. 20 cm
25. 1:16
26. 1:4
27. True
28. Same angles
29. 3
30. 12 cm and 15 cm

I hope this helps you understand similar shapes better! Remember to always check angles and proportions when identifying similar shapes. Happy learning!