Chapter 5.5, Problem 3ST2

To determine

To identify: the type of the quadrilateral $WXYZ$ .

Answer to Problem 3ST2

Rectangle

Explanation of Solution

Given:

  $\overline{WX}\cong \overline{YZ}$

  $\overline{XY}\cong \overline{ZW}$

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

Concept Used:

Theorem 5-4: the quadrilateral is a parallelogram if both pairs of opposite sides of a quadrilateral are equal.

Theorem 5-12: The diagonals of a rectangle are congruent.

It is given that for the quadrilateral $WXYZ$ , $\overline{WX}\cong \overline{YZ}$ and $\overline{WX}\parallel \overline{YZ}$

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

Thus, by theorem 5-4, the quadrilateral $WXYZ$ is a parallelogram.

Also, it is given that $\text{diag}\text{. }\overline{WY}\cong \text{diag}\text{. }\overline{XZ}$

So, by theorem 5-12, it can be said that the parallelogram $WXYZ$ is a rectangle.