Chapter 3.5, Problem 1ACYP

To determine

To state the postulate or theorem justify the answer.

  $\angle 2\cong \angle 8$

Answer to Problem 1ACYP

Theorem- when two lines are cut by a transversal and corresponding angles are congruent, then lines are parallel.

Explanation of Solution

Given information:

Figure

  $\angle 2\cong \angle 8$

Figure

In figure parallel lines are

  $a\left|\right|b$

And $l\left|\right|m$

Theorem- when two lines are cut by a transversal and corresponding angles are congruent, then lines are parallel.

From above theorem

Corresponding angle $\angle 2$ on transversal a of line l and angle $\angle 6$ on transversal b are congruent.

Then

  $\angle 2\cong \angle 6$

Further

Vertically opposite angle $\angle 6$ and $\angle 8$ are congruent

  $\angle 6\cong \angle 8$

Hence, $\angle 2\cong \angle 8$ are congruent.