Question

$▵XYZ$is isosceles with $\overline{XY}\cong \overline{XZ}$. Describe a way of mapping each point of $\overline{XY}$ to a point of $\overline{XZ}$ so that the mapping is an isometry.

Short answer

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

Step-by-step solution

Step 1. Given Information.

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

Step 2. Explanation.

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,

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

Step 3. Conclusion.

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