Question

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

$\overline{DZ}\cong \overline{BZ}$

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.

Diagonals of a parallelogram bisect each other.

Step 3. Step description.

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

From the figure, the segments $\overline{DZ},\overline{BZ}$are diagonals of a parallelogram.

Since the diagonals of a parallelogram bisect each other therefore the segments are congruent such that $\overline{DZ}\cong \overline{BZ}$.

Therefore, $\overline{DZ}\cong \overline{BZ}$must be true.