Chapter 3.3, Problem 9ST1

To determine

To the:the angles which are congruent to the angles $\angle 1$ and $\angle 9$ given that $\overline{AE}\parallel \overline{BD}$ .

Answer to Problem 9ST1

  $\angle 1\cong \angle 4$

  $\angle 9\cong \angle 3$

Explanation of Solution

Given:

The diagram:

  

Concept Used:

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent.

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Consider the given figure:

  

In this figure, it is given that lines $\overline{AE}\parallel \overline{BD}$ and using $\overline{AB}$ is a transversal, by postulate 10,

  $\angle 1\cong \angle 4$ (Corresponding angles)

Similarly, lines $\overline{AE}\parallel \overline{BD}$ and $\overline{EB}$ is a transversal, so by theorem 3-2,

  $\angle 9\cong \angle 3$ (Alternate-interior angles)