Chapter 15, Problem 17CR

To determine

To prove: that $\overline{WY}$ is not an altitude to $\overline{XZ}$ .

Answer to Problem 17CR

  $\overline{WY}$ is not an altitude to $\overline{XZ}$ .

Explanation of Solution

Given:

The given equation is $\angle X\ne \angle Z$ .

W is the mid-point of $\overline{XZ}$ .

  

Calculation:

According to the question, W is the mid-point of $\overline{XZ}$ and $\angle X\ne \angle Z$ .

Let us consider, $\overline{WY}$ is an altitude to $\overline{XZ}$ . Then,

  $\begin{array}{l}\angle XWY\cong \angle ZWY\\ \Delta XWY\cong \Delta ZWY\text{{by SAS}}\end{array}$

Therefore, by corresponding parts of congruence triangles, it is get that $\angle X=\angle Z$ .

But it is given that $\angle X\ne \angle Z$ .

So, our assumption is wrong.

Therefore, $\overline{WY}$ is not an altitude to $\overline{XZ}$ .