Question

to show that quadrilateral formed by joining the midpoints of the side of quadrilateral is a parallelogram

Answer 1

Hlo frndz. .
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In quadrilateral ABCD points P, Q, R, S are midpoints of side AB, BC, CD and AD respectively.

To prove :

PS || QR and SR || PQ. i.e. Quadrilateral PQRS is a parallelogram


Proof:

1.Draw diagonal BD.

2. As PS is the midsegment of ▲ ABD, we can say that PS || BD.

3. As QR is the midsegment of ▲ BCD, we can say that QR || BD.

4. ∵ PS || BD and QR || BD by transitivity, we can say that PS || QR.

5. Now draw diagonal AC.

6. As SR is the midsegment of ▲ ACD, we can say that SR || AC.

7. As PQ is the midsegment of ▲ ABC, we can say that PQ || AC.

8. ∵ SR || AC and PQ || AC by transitivity, we can say that SR || PQ.

9. ∵ PS || QR and SR || PQ, ∴ quadrilateral PQRS is a parallelogram


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