Answer: The correct options are
(1)∠WVX = 90°,
(2) ∠ZVY = 90°
and
(4) WY is perpendicular to ZX .
Step-by-step explanation: Given that WY and ZX are the diagonals of a kite that intersect at the point V.
We are to select the correct statements from the given options.
KITE: A quadrilateral having adjacent sides congruent and the diagonals bisect each other perpendicularly.
As shown in the attached figure, WY and ZX are the diagonals of the kite WZYX.
Since WY and ZX intersect at the point V, so they will bisect each other perpendicularly.
That is, WY is perpendicular to ZX. And, also
∠WVZ = ∠WVX = ∠ZVY = ∠XVY = 90°.
Since WZ is perpendicular to ZX, so they cannot be parallel.
Also, since the diagonals of a kite may not be equal, so WY ≠ ZX.
So, options (3) and (5) are incorrect.
Thus, the correct options are
(1)∠WVX = 90°,
(2) ∠ZVY = 90°
and
(4) WY is perpendicular to ZX .
