Question

Quadrilateral WXYZ must be a special figure to meet the conditions stated. Write the best name for that special quadrilateral.

$\overline{WX}\cong \overline{YZ},\overline{XY}\cong \overline{ZW}$and$\text{diag.}\overline{WY}\cong \text{diag.}\overline{XZ}$

Short answer

The quadrilateral is a rectangle.

Step-by-step solution

Step 1. Apply the following concept.

If both pairs of opposite sides of a quadrilateral are equal, then it's a parallelogram.

The diagonals of a rectangle are congruent.

Step 2. Step description.

Consider that $\overline{WX}\cong \overline{YZ},\overline{WX}\left|\right|\overline{YZ}$.

That is, both pairs of opposite sides of the quadrilateral are congruent.

Since one pair of the quadrilateral is parallel and congruent, therefore the quadrilateral is a parallelogram.

Step 3. Step description.

Also $\text{diag.}\overline{WY}\cong \text{diag.}\overline{XZ}$.

Since the diagonals are congruent, thus the parallelogram is a rectangle.

Therefore, the parallelogram is a rectangle.