Congruent and similar shapes Congruent shapes Similar shapes

Congruent shapes

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

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

What makes a pair of shapes “congruent”? 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

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

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

Similar shapes

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

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

What makes a pair of shapes “similar”? 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

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

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 4.5 6 3 Answers

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

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

Using scale factor Enlarge with scale factor 3 a = 9 x 3 = 27cm 9cm a 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

Similar shapes - summary b c x y z Ratio a:b:c = ratio x:y:z So: a = x a = x b = 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 SF new old 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!