Chapter 7.6, Problem 3ST2

To determine

To prove: The two triangles are similar using postulate or theorem.

Answer to Problem 3ST2

The two triangles $\text{Δ}WXV\sim \text{Δ}ZXY$ are similar with each other by the $SAS\text{ similarity theorem}$ .

Explanation of Solution

Given information:

The system triangles:

  

Calculation:

Consider two triangles $WXV$ and $ZXY$ as shown as in the textbook.

  $\angle WXV\cong \angle ZXY$

They are vertically opposite angles

Compare the corresponding sides, $\frac{WX}{ZX}=\frac{10}{15}=\frac{2}{3}$

Compare the corresponding sides, $\frac{VX}{YX}=\frac{12}{18}=\frac{2}{3}$

Thus,

  $\frac{WX}{ZX}=\frac{VX}{YX}$

  $\frac{2}{3}=\frac{2}{3}$

According to the SAS similarity theorem:

Therefore,

  $\text{Δ}WXV\sim \text{Δ}ZXY$

Hence, $\text{Δ}WXV\sim \text{Δ}ZXY$ are similar with each other by the $SAS\text{ similarity theorem}$ .