Chapter 3, Problem 30CUR

To determine

To state: the postulate or theorem which justifies the given statement, “If $\angle 2\cong \angle 3$ , then $\overline{AD}\parallel \overline{BC}$ ”

Answer to Problem 30CUR

Explanation of Solution

Given:

The diagram:

Concept Used:

Theorem 3-5: If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Consider the given figure:

From the above figure, it can be observed that the angles $\angle 2$ and $\angle 3$ are the alternate interior angles which are formed when the lines $\overline{AD}$ and $\overline{BC}$ are cut by the transversal $\overline{DB}$ .

And since $\angle 2\cong \angle 3$ , so by the theorem 3-5, it can be said that the lines $\overline{AD}$ and $\overline{BC}$ are parallel.

That is,

  $\overline{AD}\parallel \overline{BC}$