Chapter 11, Problem 4STP

To determine

To fill: The blank with the reason to state $\angle ACB\cong \angle DBC$ .

Answer to Problem 4STP

Alternate interior angles are congruent.

Explanation of Solution

Given information:

  $\overline{AC}\cong \overline{BD}$

  $\overline{AC}\left|\right|\overline{BD}$

From the given statements, it is observed that the line BD is acts as a transversal of the two parallel lines AC and BD.

Also, according to the alternate interior angles theorem, “if two parallel lines are cut by a transversal, then alternate interior angles are congruent”.

Thus, the alternate interior angles theorem proves the statement $\angle ACB\cong \angle DBC$ .

Therefore, the reason for the statement $\angle ACB\cong \angle DBC$ is alternate interior angles are congruent.