Question

on
the diagonal AC of parallelogram ABCD, there is a point Q such that CQ=1/4AC. If P is
mid-point of CD, then prove that PQ || BD.​

Answer 1

Here let BD cut AC at O.

now, OC = 1/2

AC (diagonals of a parallelogram bisect each other) ----- (1)

and CD = 1/4 AC  ----- (2)

From (1) and (2) we get

CD = 1/2 OC

in ΔDCO,  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)

Answer 2

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