Chapter 3.3, Problem 1WE

To determine

To state: the segments in the figure which are parallel given that $\angle 2\cong \angle 9$ .

Answer to Problem 1WE

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

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Consider the given figure:

From the above figure, it can be observed that the angles $\angle 2$ and $\angle 9$ are the alternate interior angles which are formed when the lines $\overline{AB}$ and $\overline{FC}$ are cut by the transversal $\overline{BF}$ .

Since it is given that

  $\angle 2\cong \angle 9$

Thus, by the theorem 3-5, it can be said that the lines $\overline{AB}$ and $\overline{FC}$ are parallel.