Question

If quadrilateral W XY Z is a parallelogram, which segment of the figure must be congruent to segment overline ZV ?

Answers

GPT-4o mini
In a parallelogram, opposite sides are congruent. Therefore, if quadrilateral WXYZ is a parallelogram, the segment opposite to \( \overline{ZV} \) must also be congruent to it.

Without more specific information about which point \( V \) lies in relation to the vertices \( W \), \( X \), \( Y \), and \( Z \) of the parallelogram, it is generally stated that segment \( \overline{WY} \) or \( \overline{XZ} \)—the sides opposite to the segment containing \( V \)—would be congruent to \( \overline{ZV} \) if those sides are in fact defined based on the same reference frame.

If \( V \) were to refer to a specific point in relation to the parallelogram—not one of the vertices—additional information would be needed to determine which segment is congruent to \( \overline{ZV} \).

In summary, opposite sides in a parallelogram are congruent, so check the segment that is opposite to \( \overline{ZV} \) to determine its congruence.

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