Question

In the adjoining figure, ABCD is a parallelogram in which P is the mid-point of CD and Q is a point on AC such that CQ = 1/4 AC. Also, PQ when produced meets BC at R. Prove that R is the mid-point of BC.​

Answer 1

Answer:

We know that the diagonals of a parallelogram bisect each other. Therefore, Therefore, according to midpoint theorem in ∆CSD PQ || DS If PQ || DS, we can say that QR || SB In ∆ CSB, Q is midpoint of CS and QR ‖ SB. Applying converse of midpoint theorem , we conclude that R is the midpoint of CB. This completes the proof.Read more on Sarthaks.com - https://www.sarthaks.com/134703/abcd-is-a-parallelogram-in-which-p-is-the-midpoint-of-dc-and-q-is-a-point-on-ac-such-that-cq-1-4-ac?show=134714#a134714