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
ZX¯¯¯¯¯¯¯¯
upper Z upper X
XV¯¯¯¯¯¯¯¯
upper X upper V
WV¯¯¯¯¯¯¯¯¯
upper W upper V
WZ¯¯¯¯¯¯¯¯¯
1 answer
In a parallelogram, the diagonals bisect each other. This means that the segments formed by the intersection of the diagonals are congruent. Therefore, since ZV is one of the segments formed by the intersection of the diagonals, segment XV must also be congruent to segment ZV.
So, the segment that must be congruent to segment ZV is:
XV (as represented by upper X upper V).
