Chapter 3.5, Problem 15PPS

To determine

To state the postulate or theorem justify the answer.

  $\angle 4\cong \angle 5$

Answer to Problem 15PPS

Theorem of corresponding angles is used.

Explanation of Solution

Given information:

Figure

  $\angle 4\cong \angle 5$

Figure

Theorem of corresponding angles

When two lines are cut by a transversal and corresponding angles are congruent, then lines are parallel.

In figure $\angle 4$ is on the line r and transversal v and $\angle 5$ is on the line s and transversal v are congruent, means lines are parallel.

In figure parallel lines are

  $r\left|\right|s$

This means $\angle 3$ and $\angle 7$ are corresponding angles.

Hence, $\angle 3\cong \angle 5$ are congruent angles.