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On your whiteboards:

On your whiteboards:. Write down the letters of a pair of shapes that are congruent. Write down the letters of a pair of shapes that are similar. On your whiteboards:. Write down the letters of a pair of shapes that are congruent. Write down the letters of a pair of shapes that are similar.

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On your whiteboards:

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  1. On your whiteboards: Write down the letters of a pair of shapes that are congruent. Write down the letters of a pair of shapes that are similar.

  2. On your whiteboards: Write down the letters of a pair of shapes that are congruent. Write down the letters of a pair of shapes that are similar.

  3. On your whiteboards: Write down the letters of a pair of shapes that are congruent. Write down the letters of a pair of shapes that are similar.

  4. What is scale factor? The enlargement of a shape is determined by its scale factor. The scale factor is the ratio of the two corresponding sides of the shapes. The shapes below are similar. What multiplier connects these lengths? 6cm 4cm

  5. What is scale factor? The enlargement scale factor is . The reduction scale factor is . What do you notice about those values? is the reciprocal of and is the reciprocal of We can also call this a multiplicative inverse. Instead of using a multiplicative inverse, we can use an inverse operation instead of the reciprocal. This means we only need to find the scale factor of enlargement. Discuss: how could we use this scale factor to find a length on the smaller shape?

  6. Scale factor Typically, we use the scale factor of enlargement rather than the scale factor of reduction. Where the lengths are corresponding sides. To find a corresponding side on the larger shape, we multiply by the scale factor. To find a corresponding side on the smaller shape, we divide by the scale factor.

  7. What is the scale factor? Find the missing lengths. Triangles not drawn to scale Example Your turn 4cm 90o 3÷2 = 1.5cm 2cm 20o 6÷3 = 2cm 80o 70o 3cm 30o 70o 3cm 80o 90o 3cm 6cm 2x2 = 4cm 4x3 = 12cm 30o 20o 70o 70o 6cm 9cm

  8. What is the scale factor? Find the missing lengths. Triangles not drawn to scale Example Your turn 4cm 20o 3÷3 = 1cm 2cm 90o 70o 9÷2 = 4.5cm 70o 3cm 80o 30o 3cm 80o 90o 3cm 6cm 3x3 = 9cm 4x2 = 8cm 20o 30o 70o 70o 9cm 6cm

  9. What is the scale factor? Find the missing lengths. Triangles not drawn to scale Example Your turn 9÷3 = 3m 14÷2 = 7m 12m 12m 10m 4.5÷3 = 1.5m 9m 10x2 = 20m

  10. Intelligent Practice – Find the length of every missing side Triangles not drawn to scale 3. 1. 2. 4. 8cm 8cm 8cm 8cm 80o 80o 80o 80o 70o 70o 70o 70o 4cm 3cm 4cm 4cm 70o 70o 70o 80o 3cm 6cm 6cm 6cm 6cm 80o 80o 70o 30o 8cm 8cm 4cm

  11. 6. 9. 8. 7. 5. 10. 4cm 4cm 8cm 8cm 8cm 8cm 60o 80o 6cm 6cm 70o 90o 4cm 4cm 4cm 4cm 90o 90o 12cm 12cm 6cm 6cm 6cm 6cm 30o 30o 3cm 2cm 2cm 4cm

  12. Practice – Find the length of every missing side Triangles not drawn to scale 4. 3. 2. 1. 6÷1 = 6cm 3÷1.5 = 2cm 6x2 = 12cm 6÷2 = 3cm 8cm 8cm 8cm 8cm 80o 80o 80o 80o 8x2 = 16cm 4÷2 = 2cm 4x1 = 4cm 70o 70o 70o 70o 4cm 4cm 4cm 4cm X1.5 x2 x1 x2 8x1.5 = 12cm 70o 70o 70o 80o 6cm 6cm 6cm 6cm 3cm 80o 80o 70o 30o 8cm 8cm 4cm

  13. 7. 10. 9. 8. 5. 6. 3÷1.5 = 2cm 6x4 = 24cm 6x2= 12cm 8cm 4cm 4cm 8cm 8cm 8cm 60o 80o Angles not the same Not similar shapes! 8÷2 = 4cm 4÷4 = 1cm 6x13 = 18cm 6cm 6cm 8x1.5 = 12cm 70o 90o 6cm 4cm 4cm 4cm 4cm x2 X1.5 x3 x4 90o 90o 12cm 12cm 6cm 6cm 6cm 6cm 30o 30o 4cm 2cm 2cm 3cm 6cm Angles not the same Not similar shapes! 18cm

  14. Exam Question Show that these two triangles are mathematically similar.

  15. Exam Question Rectangle ABCD is 15 cm by 10 cm. There is a space 5 cm wide between rectangle ABCD and rectangle PQRS. Are rectangle ABCD and rectangle PQRS mathematically similar? You must show how you got your answer.

  16. Exam Question ABD is a right-angled triangle. C is the point on BD such that angle ACB = 90°. Prove that triangle ABD is similar to triangle CBA.

  17. Exam Question A, B, C and D are four points on the circumference of a circle. AEC and BED are straight lines. Prove that triangle ABE and triangle DCE are similar. You must give reasons for each stage of your working.

  18. Prove that triangle ABE and triangle DCE are similar. You must give reasons for each stage of your working.

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