Question

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Answer 1

Answer:

See Below.

Step-by-step explanation:

We are given that PQRS is a parallelogram, where X and Y are points on the diagonal QS such that SX = QY.

And we want to prove that quadrilateral PXRY is a parallelogram.

Since PQRS is a parallelogram, its diagonals bisect each other. Let the center point be K. In other words:

$SK=QK\text{ and } PK = RK$

SK is the sum of SX and XK. Likewise, QK is the sum of QY and YK:

$SK=SX+XK\text{ and } QK=QY+YK$

Since SK = QK:

$SX+XK=QY+YK$

And since we are given that SX = QY:

$XK=YK$

So we now have:

$XK=YK\text{ and } PK=RK$

Since XY bisects RP and RP bisects XY, PXRY is a parallelogram.

Answer 2

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Join PROQ = OS (diagonals of a parallelogram bisect each other)

QY = SX OQ - QY = OS - SXOY = OX

In quadrilateral PXRYAO =  OXOX = OY

Thus, the diagonals of the quadrilateral

PXY are bisecting each other PXRY is a parallelogram.

Hope It Helped! :)

And Tell me if the answer is wrong. . .

Good Luck With Your Assignment!

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