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Congruent and similar shapes

Congruent and similar shapes. Congruent shapes. Similar shapes. Congruent shapes. Start page. 1. Which of these shapes are congruent to the yellow one?. 1. 4. 3. 2. 5. 7. 8. 6. Hints. Answers. Start page. Congruent shapes are all shown in yellow – were you right?. 1. 4.

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Congruent and similar shapes

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  1. Congruent and similar shapes Congruent shapes Similar shapes

  2. Congruent shapes

  3. Start page 1. Which of these shapes are congruent to the yellow one? 1 4 3 2 5 7 8 6 Hints Answers

  4. Start page Congruent shapes are all shown in yellow – were you right? 1 4 3 2 5 7 8 6

  5. Start page What makes a pair of shapes “congruent”? • Same angles • Same side lengths • Can be rotated or a mirror image • A cut-out of one shape will always fit exactly over the other Click the green box if you want to go back to the first “congruent shapes” question page. Question page

  6. Start page 2. Which of these shapes are congruent to the yellow one? 1 4 2 3 8 5 6 9 7 Answers

  7. Start page 4 3 8 6 9 7 Congruent shapes are all shown in yellow – were you right? 1 2 5

  8. Similar shapes

  9. Start page Which of these shapes are similar to the yellow one? 1 4 3 2 5 7 8 6 Hints Answers

  10. Start page Similar shapes are all shown in yellow – were you right? 1 4 3 2 5 7 8 6

  11. Start page What makes a pair of shapes “similar”? • Same angles • Sides in the same proportion • Can be rotated or reflected • One is an enlargement of the other • Scale factor gives degree of enlargement: • Scale factor 2 → size is doubled • Scale factor 0.5 → size is halved • Scale factor 1 → size doesn’t change → congruent too Click the green box if you want to go back to the “similar shapes” question page. Question page

  12. Start page Using similarity Since shapes are similar, their sides are in the same proportion => 6 = a 9 12 9cm 12cm Multiply both sides by 12 => 12 x 6 = a 9 6cm => a = 12 x 2 = 4 x 2 3 1 a => a = 8cm

  13. Start page Which of these shapes are similar to the yellow one?(They aren’t drawn to scale) 1 2 12 3 8 9 9 18 4 4 5 6 6 6 12 9 4.5 4 3 6 Answers

  14. Start page 1 2 12 3 8 9 18 4 4 5 6 6 12 9 4.5 4 3 6 Similar shapes are shown in yellow – were you right? 9 6

  15. Start page Scale factor? Scale factor? Scale factor = new value old value. New value = Old value 12 = 3 or 1.5 8 2 8cm 12cm 5cm New value = Old value 8 = 2 12 3 7.5cm Can you see the relationship between the two scale factors?

  16. Start page Using scale factor Enlarge with scale factor 3 a = 9 x 3 = 27cm 9cm a What will the scale factor be? b SF = new/old = 9/27 = ⅓ OR reciprocal of 3 = ⅓ 15cm b = 15 x ⅓ = 15 ÷ 3 = 5cm

  17. Similar shapes - summary c a z x b y new SF old Ratio a:b:c = ratio x:y:z So: a = xa = xb = y b y c z c z To see whether 2 shapes are similar, put each ratio in its simplest form and see if they match. Scale factor = new measurement old measurement Old measurement x SF = new measurement • - Scale factor more than 1 => shape gets bigger • Scale factor less than 1 => shape gets smaller • Congruent shapes are similar shapes with SF = 1 Remember: only side lengths change; angles stay the same!

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