Chapter 7.4, Problem 14PPS

To determine

To explain:

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

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

Answer to Problem 14PPS

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

Explanation of Solution

Given information:

  

  $\begin{array}{l}ZX=18\\ ZV=6\\ WX=24\\ YX=16\end{array}$

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,

  $\begin{array}{l}\frac{WY}{YX}=\frac{ZV}{VX}\\ \frac{WX-YX}{YX}=\frac{ZV}{ZX-ZV}\\ \frac{24-16}{16}=\frac{6}{18-6}\\ \frac{1}{2}=\frac{1}{2}\end{array}$

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