Chapter 3.5, Problem 13PPS

To determine

To state the postulate or theorem justify the answer.

  $\angle 3\cong \angle 5$

Answer to Problem 13PPS

Theorem of alternate co-interior angles is used.

Explanation of Solution

Given information:

Figure

  $\angle 3\cong \angle 5$

Figure

Theorem of alternate co-interior angles

When two lines are cut by a transversal and alternate co-interior angles are congruent, then lines are parallel.

In figure $\angle 3$ is on the line u and transversal s and $\angle 5$ is on the line v and transversal s are congruent, means lines are parallel.

In figure parallel lines are

  $u\left|\right|v$

This means $\angle 3$ and $\angle 5$ are alternate co-interior angles.

Hence, $\angle 3\cong \angle 5$ are alternate co-interior angles.