Question

ABCD is a quadrilateral and P,Q,R and S are the midpoints of AB,BC,CD and AD respectively. If length of PQ=4cm,find length of RS?
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Answer 1

Answer:

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=21AC.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=21AC.By mid-point theorem. But from (i) SR=21AC 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.