1. 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

2. 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

3. 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

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

5. 21 cm
6 cm a b
10 cm
9 cm
what is the multiplier?

6. pair off the similar triangles and state the scale factor15 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

7. 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