Similarity vs Congruence Two shapes are congruent if: ! ? They are the same shape and size (flipping is allowed) Two shapes are similar if: ! ? They are the same shape (flipping is again allowed) b b b a a a

Similarity These two triangles are similar. What is the missing length, and why? 5 ? 7.5 8 12 There’s two ways we could solve this: The ratio of the left side and bottom side is the same in both cases, i.e.: 5 8 = 𝑥 12 Find scale factor: 12 8 Then multiply or divide other sides by scale factor as appropriate. 𝑥=5× 12 8

Quickfire Examples Given that the shapes are similar, find the missing side (the first 3 can be done in your head). 1 2 10 12 ? 32 ? 24 15 18 15 20 4 3 17 24 11 20 40 25 ? 25.88 ? 30

two triangles are similar if their three angles are the same 21 cm a 6 cm b 12 cm 18 cm

21 cm 6 cm a b 10 cm 9 cm what is the multiplier?

pair off the similar triangles and state the scale factor 15 15 B 18 15 15 15 C 12 9 D 15 A 12 24 7.5 15 E 15 20 20 F 10 15 19.2 10 13.5 G H 12.8 10.5 16 20 20 K 8 6 L 12 8 10 6 M 6 N 10 16 6 32 32 12 12 20 18 P 18 Q 15 R S 18 14 24 12

A B C < < < D E A A B B < < < < D E D E C C ABC and ADE have all three angles the same A B C < < < D E A A B B < < < < D E D E C C