Question

The diagonals of $▱ABCD$ intersecting at Z. For the following figure, tell whether the statement must be, maybe, or cannot be true.

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

Short answer

The statement must be true.

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of the parallelogram.

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

Step 3. Step description.

Consider ABCD is a parallelogram and diagonals AB and CD intersect at Z.

The segments $\overline{AD},\overline{BC}$are the diagonals of a parallelogram.

Since a quadrilateral is a parallelogram if both pairs of opposite sides are congruent thus $\overline{AD}\parallel \overline{BC}$.

Therefore, $\overline{AD}\parallel \overline{BC}$must be true.