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P and Q are respectively the mid-points...

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and Ris the mid-point of AP, show that (i) `a r (P R Q)=1/2a r(A R C)`(ii) `a r (R Q C)=3/8a r (A B C)`(iii) `a r (P B Q) =a r (ARC)`

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To solve the problem step by step, we will show the required results one by one. ### Given: - P and Q are the midpoints of sides AB and BC of triangle ABC. - R is the midpoint of segment AP. ### To Prove: 1. \( \text{Area} (P R Q) = \frac{1}{2} \text{Area} (A R C) \) ...
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