Exercise 84 Page 116

Practice makes perfect

a If two triangles are similar, they have the same shape which means corresponding angles are congruent. By the Triangle Sum Theorem, we know that the sum of a triangles angles is 180^(∘). With this, we can calculate the unknown angle in each triangle.

180^(∘)-60^(∘)-40^(∘)&=80^(∘) 180^(∘)-60^(∘)-85^(∘)&=35^(∘) Let's add these angles to the figure.

Since the two triangles don't have three pairs of congruent corresponding angles, they are not similar.

b Like in Part B, we will calculate the unknown angles.

180^(∘)-50^(∘)-45^(∘)&=85^(∘) 180^(∘)-50^(∘)-85^(∘)&=45^(∘) Let's add these angles to the figure.

Since the two triangles have three pairs of congruent corresponding angles, they are similar.

c Similar figures preserves ratios of length. Therefore, if we divide corresponding sides, all of these ratios should be the same if the triangles are similar. Notice that in similar figures, the shortest sides are corresponding, the longest sides are corresponding and so on. With this, we can identify corresponding sides.

Having identified corresponding sides, we can write an equation. 6/12? =8/16? =7/14 By calculating the three ratios, we can determine if the triangles are similar. 0.5= 0.5= 0.5 Since the ratio of all sides are equal, the triangles are similar.