Chapter 3.5, Problem 1DCYP

To determine

To state the postulate or theorem justify the answer.

  $\angle 1\cong \angle 15$

Answer to Problem 1DCYP

Theorem of exterior alternate angles

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

Explanation of Solution

Given information:

Figure

  $\angle 1\cong \angle 15$

Figure

Theorem of exterior alternate angles

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

From above theorem

Corresponding angle $\angle 1$ on transversal a of line l and angle $\angle 15$ on transversal b and line m are congruent.

Then lines l and m are parallel.

  $l\left|\right|m$

Then

  $\angle 1\cong \angle 15$

Hence, $\angle 1\cong \angle 15$ are congruent.