# Chapter 7 - Similarity - Mid-Chapter Quiz - Page 459: 12

No, the triangles are not similar because two sides in one triangle are not proportional to two sides in the other triangle since they have different scale factors.

#### Work Step by Step

We are given the measures of two sides in the two triangles. Additionally, we can see that there is a pair of vertical angles, one belonging to each triangle. We know that vertical angles are congruent. Let's see if the Side-Angle-Side Similarity Theorem can be applied here. The SAS Similarity Theorem states that if two sides in one triangle are proportional to the two sides of another triangle, and the included angle in one triangle is congruent to the included angle of the other triangle, then the two triangles are similar. Let's set up the ratios of corresponding sides in $\triangle WXV$ and $\triangle ZXY$: $\frac{WX}{ZX} = \frac{8}{2}$ Divide both the numerator and denominator by their greatest common factor, $2$: $\frac{WX}{ZX} = \frac{4}{1}$ Let's look at $XV$ and $XY$: $\frac{XV}{XY} = \frac{9}{3}$ Divide both the numerator and denominator by their greatest common factor, $3$: $\frac{XV}{XY} = \frac{3}{1}$ Let's look at the vertical angles in the two triangles: $m \angle WXV ≅ m \angle ZXY$ They are not similar.

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