Chapter 3.5, Problem 1CCYP

To determine

To state the postulate or theorem justify the answer.

  $\angle 12\cong \angle 14$

Answer to Problem 1CCYP

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

Definition of vertically opposite angles.

Explanation of Solution

Given information:

Figure

  $\angle 12\cong \angle 14$

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 cingruent, then lines are parallel.

From above theorem

Corresponding angle $\angle 12$ on transversal a of line m and angle $\angle 16$ on transversal b of line m are congruent.

Then

  $\angle 12\cong \angle 16$

Then

Angle $\angle 16$ and angle $\angle 14$ are vertically opposite angles

Hence, $\angle 12\cong \angle 14$ are congruent.