Exercise 99 Page 192

Practice makes perfect

a Examining the diagram, we see that we are only given the triangle's side lengths. Therefore, we will not be able to use SAS Similarity or AA Similarity to prove similarity because they require us to have information about the triangle's angles.

However, having all three sides of the triangles allows us to use SSS Similarity. Let's identify the triangles corresponding sides.

Having identified corresponding sides, we can write an equation that relates the ratios. 3/3.6? =5/6? =4/4.8 By calculating the three ratios, we can show that the triangles are similar. 0.8333...= 0.8333...= 0.8333... Since the ratio of all sides are equal, the triangles are similar.

b These triangles have two pairs of congruent corresponding angles. Therefore, we can definitely use AA Similarity to show similarity. Also, since we do not know all three sides, we can definitely not use SSS Similarity.

To use SAS Similarity, we need to show that the ratio between corresponding sides is the same. Let's identify the triangles corresponding sides.

Having identified corresponding sides, we can write an equation that relates the ratio of these. 3.5/7? =2/4 By calculating the two ratios, we can show that the triangles are similar. 0.5= 0.5 Since the ratio of the two corresponding sides are equal, and the sides included angles are congruent, we know that these triangles are similar by SAS Similarity.

c The similarity conditions require you to know the following.

AA~ ⇒ &You need to know two &congruent corresponding angles SSS~ ⇒ &You need to know all three sides SAS~ ⇒ &You need to know two corresponding &sides and the included angle However, we only know an angle in one triangle and a side in each triangle. For this reason, we cannot claim that the triangles are similar.