Chapter 5.5, Problem 1ST2

To determine

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

Answer to Problem 1ST2

Parallelogram

Explanation of Solution

Given:

  $\overline{WX}\cong \overline{YZ}$

  $\overline{WX}\parallel \overline{YZ}$

Concept Used:

Theorem 5-5: If one pair of opposite sides of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram.

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

That is, one pair of opposite sides of a quadrilateral $\overline{WX}$ and $\overline{YZ}$ are both congruent and parallel.

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