Chapter 4.4, Problem 27PPS

To determine

The value of the variable that yields congruent triangles.

Answer to Problem 27PPS

Value of y = 4 yields congruent triangles.

Explanation of Solution

Given:

  $\Delta WXY\cong \Delta WXZ$

  

Calculation:

According to CPCTC (Corresponding Parts of Corresponding Triangles are Congruent) $\overline{XY}\cong \overline{XZ}\text{ and }\angle \text{WXZ}\cong \angle WXY.$

Therefore,

  $\begin{array}{l}XZ=XY\\ 3y+7=19\\ 3y=12\\ y=\frac{12}{3}\\ y=4\end{array}$

The measure of angle WXY is:

  $\begin{array}{l}m\angle WXY=20y+10\\ m\angle WXY=20\left(4\right)+10\\ m\angle WXY=90\end{array}$

This proves that $\text{m}\angle \text{WXY= m}\angle WXZ.$

Hence, value of y = 4 yields congruent triangles.