Question

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$\overline{AD}\cong \overline{BC}$

Short answer

The theorem that justifies the statement $\overline{AD}\cong \overline{BC}$is the theorem 5-1 which states that opposite sides of a parallelogram are congruent.

Step-by-step solution

Step 1. Observe the diagram.

The given diagram is:

Step 2. Description of step.

The theorem 5-1 states that opposite sides of a parallelogram are congruent.

It is being given that quadrilateral ABCD is a parallelogram.

From the given diagram it can be noticed that the sides $\overline{AD}$ and $\overline{BC}$ are the opposite sides of the parallelogram ABCD.

Therefore, by using the theorem 5-1 it can be said that $\overline{AD}=\overline{BC}$.

Therefore, $\overline{AD}\cong \overline{BC}$.

Step 3. Write the theorem that justifies the statement.

Therefore, the theorem that justifies the statement $\overline{AD}\cong \overline{BC}$is the theorem 5-1 which states that opposite sides of a parallelogram are congruent.