Question

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

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

Short answer

The definition that justifies the statement $\overline{AD}\parallel \overline{BC}$is the definition of the parallelogram which states that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

Step-by-step solution

Step 1. Observe the diagram.

The given diagram is:

Step 2. Description of step.

Definition of parallelogram states that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.

It is being given that $\overline{AD}\parallel \overline{BC}$.

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

As, $\overline{AD}\parallel \overline{BC}$, therefore it can be said that the opposite sides of the quadrilateral ABCDare parallel.

Therefore, it can be said that $\overline{AD}\parallel \overline{BC}$by using the definition of a parallelogram.

Step 3. Write the definition that justifies the statement.

Therefore, the definition that justifies the statement $\overline{AD}\parallel \overline{BC}$is the definition of the parallelogram which states that a parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.