Question

in parallelogram PQRS, PR=PQ , X , Y are the midpoints of QR, PS. Prove that YRXP is a rectangle​

Answer 1

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Suppose XY and diagonal QS intersect each other at point O.

Since X and Y are the midpoints of PS and QR. This means XY is parallel to PQ.

Now in triangle PQS, XO is parallel to PQ And X is midpoint of PS. By applying midpoint theorem on triangle PQS, O becomes midpoint of QS.

So, XY devides QS in the ration 1:1.

Answer 2

Suppose XY and diagonal QS intersect each other at point O.

Since X and Y are the midpoints of PS and QR. This means XY is parallel to PQ.

Now in triangle PQS, XO is parallel to PQ And X is midpoint of PS. By applying midpoint theorem on triangle PQS, O becomes midpoint of QS.

So, XY devides QS in the ration 1:1.

So, correct answer is option B.

solution

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