Question

4) ABCD is a quadrilateral. P,Q,R,S are the midpoints of the sides AB, BC, CD and DA respectively. If AC=6cm. BD-8.6cm, then find PQ, QR, RS, and SP.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

(i) In △DAC , S is the mid point of DA and R is the mid point of DC. Therefore, SR∥AC and SR=1/2

AC.By mid-point theorem.

(ii) In △BAC , P is the mid point of AB and Q is the mid point of BC. Therefore, PQ∥AC and PQ=1/2 AC.By mid-point theorem. But from (i) SR=1/2

AC therefore PQ=SR

(iii) PQ∥AC & SR∥AC therefore PQ∥SR and PQ=SR. Hence, a quadrilateral with opposite sides equal and paralle is a parallelogram. Therefore PQRS is a parallelogram.

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