Chapter 14.3, Problem 20WE

To determine

To construct:A segment $\overline{XY}$ parallel & congruent to $\overline{CD}$ .

Answer to Problem 20WE

A segment $\overline{XY}$ parallel & congruent to $\overline{CD}$ is constructed.

Explanation of Solution

Given information :

$\odot A$ and $\odot B$ along with $\overline{CD}$ .

Concept used:

For segment to be parallel the slope must be same & for congruent the length must be same.

$\odot A$ and $\odot B$ along with $\overline{CD}$ .

Below diagram is provided in problem.

We will construct the required line segment parallel & congruent.

  $\begin{array}{l}\overline{XY}=\overline{CD}\\ \angle X=\angle C\\ \angle Y=\angle D\end{array}$

Hence,

A segment $\overline{XY}$ parallel & congruent to $\overline{CD}$ is constructed& having $X$ on $\odot A$ and $Y$ on $\odot B$ .