Chapter 5.6, Problem 6PSA

To determine

To prove:

ABCDis aparallelogram.

Explanation of Solution

Given information:

  $\overline{CD }\parallel \overline{AB }$ .

  $\angle EDA\cong \angle CBF$ .

Proof:

  

It is given that,

  $\overline{CD }\parallel \overline{AB }$ .

  $\angle EDA\cong \angle CBF$ .

If lines are parallel then their alternate interior angles are congruent.

  $\begin{array}{l}\angle A\cong \angle EDA\\ \angle C\cong \angle CBF\end{array}$

By substitution property, we get

  $\angle C\cong \angle A$

Supplementary angles form a straight angle.

  $\angle CDA$ is supplementary of $\angle EDA$ .

  $\angle CBA$ is supplementary of $\angle CBF$ .

Supplementary of congruent angles are congruent.

  $\angle CDA\cong \angle CBA$

If both pairs of opposite angles are congruent, a quadrilateral is a parallelogram.

ABCD is a parallelogram.