Chapter 7.4, Problem 17PPS

To determine

To explain:

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

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

Answer to Problem 17PPS

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:

  

  $\begin{array}{l}WX=31\\ YX=21\\ ZX=4ZV\end{array}$

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:

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

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

  $\begin{array}{l}\frac{WY}{YX}=\frac{WX-YX}{YX}\\ \frac{WY}{YX}=\frac{31-21}{21}\\ \frac{WY}{YX}=\frac{10}{21}\end{array}$

And

  $\begin{array}{l}\frac{ZV}{VX}=\frac{ZV}{ZX-ZV}\\ \frac{ZV}{VX}=\frac{ZV}{4ZV-ZV}\\ \frac{ZV}{VX}=\frac{ZV}{3ZV}\\ \frac{ZV}{VX}=\frac{1}{3}\end{array}$

Here, $\begin{array}{l}\frac{WY}{YX}\ne \frac{ZV}{VX}\\ \frac{10}{21}\ne \frac{1}{3}\end{array}$

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