Chapter 3.3, Problem 3WE

To determine

To state: the segments in the figure which are parallel given that $m\angle 1=m\angle 8=90$ .

Answer to Problem 3WE

  $\overline{AB}\parallel \overline{FC}$

Explanation of Solution

Given:

The diagram:

Concept Used:

Postulate 11: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Consider the given figure:

From the above figure, it can be observed that the angles $\angle 1$ and $\angle 8$ are the corresponding angles which are formed when the lines $\overline{AB}$ and $\overline{FC}$ are cut by the transversal $\overline{AE}$ .

Since it is given that

  $m\angle 1=m\angle 8=90$

It implies that, the corresponding angles $\angle 1$ and $\angle 8$ are congruent.

Thus, by the postulate 11, it can be said that the lines $\overline{AB}$ and $\overline{FC}$ are parallel.