The given parallelogram is a rectangle when ΔZYX ≅ ΔWXY.
What is a parallelogram?
"A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure."
In the given parallelogram WXYZ,
ZX ≅ WY.
For ΔZXY and ΔWXY,
ZX = WY (already given)
ZY = WX (two opposite sides of the parallelogram WXYZ)
XY is the common side
Therefore, ΔZXY ≅ ΔWXY
Now, we can say, ∠ZYX = ∠WXY
However, for the given parallelogram, ∠ZYX + ∠WXY = 180°
Therefore, ∠ZYX = ∠WXY = 90°
Hence, the parallelogram given is a rectangle.
Learn more about a parallelogram here: https://brainly.com/question/11220936
#SPJ3
