Chapter 7.4, Problem 15PPS

To determine

To explain:

The following condition is satisfied by $△WZX$ or not:

  $\overline{VY}\parallel \overline{ZW}$

Answer to Problem 15PPS

Yes, $\overline{VY}\parallel \overline{ZW}$ condition successfully satisfied by $△XZW$ as $\frac{WY}{YX}=\frac{ZV}{VX}$ .

Explanation of Solution

Given information:

  

  $\begin{array}{l}VX=7.5\\ ZX=24\\ WY=27.5\\ WX=40\end{array}$

Need to use the triangle proportionality theorem to satisfy the condition of $\overline{VY}\parallel \overline{ZW}$ for $△XZW$ :

  $\frac{WY}{YX}=\frac{ZV}{VX}$

Know that:

  $\begin{array}{l}WX=WY+YX\\ ZX=ZV+VX\end{array}$

So,

  $\begin{array}{l}\frac{WY}{YX}=\frac{ZV}{VX}\\ \frac{WY}{WX-WY}=\frac{ZX-VX}{VX}\\ \frac{27.5}{40-27.5}=\frac{24-27.5}{7.5}\\ \frac{27.5}{12.5}=\frac{16.5}{7.5}\\ 2.2=2.2\end{array}$

Therefore, $\overline{VY}\parallel \overline{ZW}$ condition successfully satisfied by $△XZW$ as $\frac{WY}{YX}=\frac{ZV}{VX}$ .