Use the image to answer the question.

Question

A parallelogram has vertices upper W, upper X, upper Y, and upper Z. Opposite vertices are connected via diagonal lines that intersect at an interior point labeled upper V. Sides upper W upper X and upper Z upper Y are longer than the other sides.

If quadrilateral WXYZ
is a parallelogram, which segment of the figure must be congruent to segment ZV¯¯¯¯¯¯¯¯
?

(1 point)
Responses

WZ¯¯¯¯¯¯¯¯¯
upper W upper Z

WV¯¯¯¯¯¯¯¯¯
upper W upper V

XV¯¯¯¯¯¯¯¯
upper X upper V

ZX¯¯¯¯¯¯¯¯
upper Z upper X
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Answer 1

In a parallelogram, the diagonals bisect each other. This means that the point of intersection (point V in this case) divides each diagonal into two congruent segments.

Since segment \( ZV \) is one half of diagonal \( ZY \), its corresponding segment on the other diagonal \( WX \) would be \( WV \). Therefore, segment \( WV \) must be congruent to segment \( ZV \).

The correct response is:

WV (segment \( \overline{WV} \)).