Chapter 7.4, Problem 16PPS

To determine

To explain:

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

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

Answer to Problem 16PPS

No, $\overline{VY}\parallel \overline{ZW}$ condition is not satisfied by $△XZW$ as $\frac{WY}{YX}\ne \frac{ZV}{VX}$ .

Explanation of Solution

Given information:

  

  $\begin{array}{l}ZV=8\\ VX=2\\ YX=\frac{1}{2}WY\end{array}$

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

  $\frac{WY}{YX}=\frac{ZV}{VX}$

Now, check the value of $\frac{WY}{YX}$ :

  $\begin{array}{l}\frac{WY}{YX}=\frac{WY}{\frac{1}{2}WY}\\ \frac{WY}{YX}=2\end{array}$

And

  $\begin{array}{l}\frac{ZV}{VX}=\frac{8}{2}\\ \frac{ZV}{VX}=4\end{array}$

Here, $\begin{array}{l}\frac{WY}{YX}\ne \frac{ZV}{VX}\\ 2\ne 4\end{array}$

Therefore, $\overline{VY}\parallel \overline{ZW}$ condition is not satisfied by $△XZW$ as $\frac{WY}{YX}\ne \frac{ZV}{VX}$ .