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In parallelogram ABCD, P and Q are the mid-points ofDC and BC respectively. Prove that CR = 1/4 AC |
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Answer» Here let BD cut AC at O.now, OC = 1/2AC (diagonals of a parallelogram bisect each other) ----- (1)and CD = 1/4 AC ----- (2)From (1) and (2) we getCD = 1/2 OCinΔDCO, and Q are midpoints of DC and OC respectively∴PQ║DO ( midpoint theorem)Also in ΔCOB Q is the midpoint of OC and PQ║AB∴R is the midpoint of BC (converse of midpoint theorem) |
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