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

A. overline XV
B. overline WV
C. Over line WZ
D. overline ZX

1 answer

In a parallelogram, opposite sides are congruent. Given that quadrilateral WXY Z is a parallelogram, we know that:

  • \( \overline{WX} \cong \overline{YZ} \)
  • \( \overline{XY} \cong \overline{WZ} \)

Since you are looking for a segment that must be congruent to segment \( \overline{ZV} \), we identify that if \( \overline{ZV} \) is a segment extending from vertex Z, the only congruent segment would be the one that corresponds to it directly in the parallelogram.

Therefore, you would typically compare this segment to one of the other sides of the parallelogram. If \( \overline{ZV} \) represents a specific vector related to the positioning or connection within the parallelogram, one might infer that the segment across from it (which could be designated within the context of the problem as \( \overline{WV} \) given the layout of a parallelogram, where the figure layout is comprehensively understood) would maintain congruence.

Thus, the correct answer based on the properties of parallelograms would be:

B. \( \overline{WV} \)

This is because \( \overline{WV} \) would be directly opposite \( \overline{ZV} \) if we consider typical vector relationships.

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