Congruent and similar shapes Congruent shapes 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 3 4 2 6 7 Hints 8 5 Answers

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

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

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

Similar shapes

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

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

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 9 cm Multiply both sides by 12 => 12 x 6 = a 9 6 cm => a = 12 x 2 = 4 x 2 3 1 => a = 8 cm 12 cm a

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

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

Start page Scale factor = new value old value. Scale factor? New value = 12 = 3 or 1. 5 Old value 8 2 12 cm 8 cm Scale factor? 5 cm New value = 8 = 2 Old value 12 3 7. 5 cm Can you see the relationship between the two scale factors?

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

Similar shapes - summary Ratio a: b: c = ratio x: y: z So: a = x a=x b=y z x b y c z b To see whether 2 shapes are similar, put each y ratio in its simplest form and see if they match. Scale factor = new measurement new old measurement c a Old measurement x SF = new measurement SF old - 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!