Exercise 12 Page 459

Let's review the theorems that can help us prove that two triangles are similar.

1. Angle-Angle Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
2. Side-Side-Side Similarity Theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar.
3. Side-Angle-Side Similarity Theorem: If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

Notice that there is a pair of vertical angles. These angles have equal measures.

Notice that ∠ X is the included angle between two known sides in each triangle. We also know the lengths of these sides. Let's check if they are proportional. cccc XZ/WX & = & 2/8 & = & 1/4 [0.8em] XY/VX & = & 3/9 & = & 1/3 As we can see, the ratios are not equal. Therefore, the corresponding sides are not proportional and the given triangles are not similar.