Similar & Congruent Shapes Thursday, 04 April 2019

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

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.

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

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

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

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

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

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

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

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

E B 12 cm 6 cm D C A 15 cm

S 34° P 23° R Q T