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2. 2 shapes which are identical are called: Congruent Which transformations produce congruent images? Congruent shapes have: Equal lengths angles areas

3. © T Madas 2 shapes are called similar if : One is the enlargement of the other Which transformation produces similar images? similar shapes have: Equal angles

4. © T Madas The ratio of lengths of similar shapes is equal to: the scale factor a A S.F. = 2 2 shapes are called similar if : One is the enlargement of the other A a = 2= 2

5. © T Madas 6 cm 12 cm 8 cm 20 cm The two triangles below are similar. Find their missing sides. What is the scale factor? x2x2 x2x2 ÷2÷2 10 cm 16 cm

6. © T Madas 6 cm 18 cm The two shapes below are similar. Find their missing sides. What is the scale factor? x3x3 7 cm 15 cm 8 cm 21 cm 24 cm 5 cm

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8. 3 5 x 15 9 4 y12 5 x 20 16 3 9 y 6 x 42 49 63 7 10 16 12 z 15 y x 30 24 18 20 Calculate the missing lengths in each diagram figures not to scale measurements in cm

9. © T Madas 7 9 x 54 42 12 y20 13 x 52 48 5 9 y 8 x 72 56 81 7 10 16 12 z 25 y x 50 40 30 20 Calculate the missing lengths in each diagram figures not to scale measurements in cm

10. © T Madas 2 4 x 9 4.5 3 y 6 x 18 27 9 9 10 20 15 z 16 y x 40 32 24 25 Calculate the missing lengths in each diagram figures not to scale measurements in cm

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12. 3 5 x 15 9 4 y12 5 x 20 16 3 9 y 6 x 42 49 63 7 10 16 12 z 15 y x 30 24 18 20 Calculate the missing lengths in each diagram figures not to scale measurements in cm

13. © T Madas 7 9 x 54 42 12 y20 13 x 52 48 5 9 y 8 x 72 56 81 7 10 16 12 z 25 y x 50 40 30 20 Calculate the missing lengths in each diagram figures not to scale measurements in cm

14. © T Madas 2 4 x 9 4.5 3 y 6 x 18 27 9 9 10 20 15 z 16 y x 40 32 24 25 Calculate the missing lengths in each diagram figures not to scale measurements in cm

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16. Angles are equal Lengths are multiplied by the scale factor Areas are multiplied by the scale factor squared x2x2 x3x3 If two shapes are similar:

17. © T Madas Angles are equal Lengths are multiplied by the scale factor Areas are multiplied by the scale factor squared If two shapes are similar: S.F. = 2 Lengths: x2x2 Area:x22x22 = x4= x4

18. © T Madas Angles are equal Lengths are multiplied by the scale factor Areas are multiplied by the scale factor squared If two shapes are similar: S.F. = 3 Lengths: x3x3 Area:x32x32 = x9= x9

19. © T Madas Angles are equal Lengths are multiplied by the scale factor Areas are multiplied by the scale factor squared If two shapes are similar: S.F. = 1.5 Lengths: x1.5 Area:x1.5 2 = x2.25

20. © T Madas If 2 shapes are similar: All lengths are multiplied by the scale factor Consider a triangle enlarged by a scale factor s b sb h sh F o r m a l P r o o f

21. © T Madas If 2 shapes are similar: All lengths are multiplied by the scale factor F o r m a l P r o o f Every polygon can be split into triangles so the result holds in general

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23. A shape with an area of 16 cm 2 is enlarged by a scale factor of 4½. Calculate the area of the enlarged shape. The enlarged shape has an area of 324 cm 2 Scale factor s = 4.5

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25. A pyramid has a height of 10 cm and a surface area of 200 cm 2. A similar pyramid has a height of 25 cm. Find the surface area of the larger pyramid. The larger pyramid has a surface area of 1250 cm 2 Scale factor s =2.5

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27. A cylinder has a surface area of 18225 cm 2 and a radius of 9 cm. A similar cylinder has a radius of 2 cm. Find the surface area of the smaller cylinder. The smaller cylinder has a surface area of 900 cm 2 Scale factor s =4.5

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29. Two similar shapes P and Q have areas of 20 cm 2 and 1125 cm 2 respectively. Calculate the scale factor from P to Q. The scale factor from P to Q is 7.5

31. Angles are equal Lengths are multiplied by the scale factor Areas are multiplied by the scale factor squared If two shapes are similar: Volumes are multiplied by the scale factor cubed

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33. A cone has volume 100 cm 3 and height of 10 cm. A similar cone has a height of 15 cm. Calculate the volume of the larger cone. The larger cone has a volume of 337.5 cm 3 Scale factor s =1.5

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35. A prism has a height of 10 cm. A similar prism has a height of 20 cm and a volume of 1000 cm 3. Calculate the volume of the smaller prism. The smaller prism has a volume of 125 cm 3 Scale factor s =2

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