Chapter 14.3, Problem 21WE

To determine

To construct:Points $X$ and $Y$ on the lines shown so that $\overline{XY}$ parallel to $\overline{EF}$ .

Answer to Problem 21WE

A segment $\overline{XY}$ parallel & congruent to $\overline{EF}$ is constructed & having $X$ and $Y$ on each line shown.

Explanation of Solution

Given information :

Two lines are shown & line segment $\overline{EF}$ .

Concept used:

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

Two lines are shown & line segment $\overline{EF}$ .

Below diagram is provided in problem.

We will construct the required line segment parallel & congruent.

$\overline{EF}$ segment drag towards to the line shown in the figure $\overline{CD}$ and $\overline{GH}$ , we get the intersection point on both the line, thus we get line segment $\overline{XY}$ .

When we drag the line, orientation remain the same & length remain unchanged. $\overline{XY}$ is thus parallel & congruent to $\overline{EF}$ .

Hence,

A segment $\overline{XY}$ parallel & congruent to $\overline{EF}$ is constructed& having $X$ and $Y$ on each line shown.