Chapter 14.1, Problem 12WE

To determine

To find: The way of mapping for each point of $\overline{XY}$ to a point of $\overline{XZ}$ so that the mapping is an isometry.

Answer to Problem 12WE

The mapping of each point of $\overline{XY}$ to a point of $\overline{XZ}$ .

Explanation of Solution

Given information:

It is given that $\Delta XYZ$ is isosceles with $\overline{XY}\cong \overline{XZ}$ is the mapping of an isometry.

  

Calculation:

Draw a point $A$ on sides $\overline{XY}$ and $A\text{'}$ on $\overline{XZ}$ they will be similar from both points $X$ to same on sides

From the figure, $\Delta XYZ$ is isosceles. So,

  $\overline{XY}\cong \overline{YZ}\cong \overline{XZ}$

  

Therefore, the mapping of each point of $\overline{XY}$ to a point of $\overline{XZ}$ is the mapping of an isometry.