Chapter 5.1, Problem 12CE

To determine

To state: the theorem or definition which justifies the given statement, “ $\overline{AD}\cong \overline{BC}$ ”

Answer to Problem 12CE

Theorem 5-1

Explanation of Solution

Given:

The diagram:

  $ABCD$ is a parallelogram.

Concept Used:

Theorem 5-1: Opposite sides of a parallelogram are congruent.

Consider the given figure:

It is given that $ABCD$ is a parallelogram.

So by theorem 5-1, opposite sides of parallelogram $ABCD$ are congruent.

In this figure it can be observed that $\overline{AB}$ , $\overline{CD}$ and $\overline{AD}$ , $\overline{BC}$ are the pairs of opposite sides of the parallelogram $ABCD$ .

Thus by theorem 5-1,

  $\overline{AD}\cong \overline{BC}$