1. Similar & Congruent Shapes
Thursday, 04 April 2019

2. Example
Several triangles are drawn here. Calculate the missing angle and decide which are similar triangles.
(a) (b) (c)
(d) (e) (f) 40 c 65 b 50 a 65 50 d 45
120 f 45 25 e

3. IN general
Similar figures have the same shape but different sizes. In other words the only difference is that one is an enlargement of the other.
A shape is said to be congruent if they have the same shape and same size. In other words two identical shapes are said to be congruent.

4. What are the sizes of the lettered angles
Example
For the diagram below
What are the sizes of the lettered angles
Do the triangles ABC and CDE have the same angles. Comment? A C D E B 70 x y z w

5. Decide whether triangles PQR and PST are similar ot not.
Example
Decide whether triangles PQR and PST are similar ot not. Q R 50 30 P T S

6. Hence calculate the missing side
Example
By finding the unknown angles show that the following two triangles are similar.
Hence calculate the missing side
3 cm 27 63
12 cm x b a
6 cm

7. Example
Prove that the triangles ABC and ADE are similar
Hence obtain the length BC in the diagram below A D B E C
2 cm
7.5 cm
4 cm

8. Example
Given that the following pair are similar, find the lengths of the lettered sides.
4cm 𝑦
24cm
10cm
15cm 𝑥

9. Example
Given that these two triangles are congruent, work out the lettered values. 𝑥 𝑐
34° 𝑎
15 cm
34°
14 cm 𝑦 𝑏
79° 𝑢
6 cm

10. In the diagram, the lines AE and BD intersect at C.
Example
In the diagram, the lines AE and BD intersect at C.
Given that AB = DE show that the triangles ABC and CDE are congruent. A B C D E

12. A B C D E F G H 𝑥
67°
9 𝑐𝑚 𝑦
7𝑐𝑚
65°
65° 𝑤

13. E B
12 cm
6 cm D C A
15 cm

14. S
34° P
23° R Q T