Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY.
1 answer:
A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.
<h3>What is a parallelogram?</h3>A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
For a parallelogram, the opposite sides are equal and parallel to each other. We can write,
AD ≅ BC
Since BX ≅ DY, therefore, we can write,
AB = CD
AX + XB = DY + YC
XB = DY, cancelling both the sides,
AX = YC.
Also, XY is the common side.
Since all the sides are equal also the angle are equal, therefore, it can be written,
AXDY ≅ CYXB
Given the area of CYXB is 71.5 square units. Therefore,
ABCD = CYXB + AXDY
ABCD = 2(CYXB)
ABCD = 143 square units.
Hence, the correct option is D.
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