ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such - Maths - Quadrilaterals

Question

ABCD is a parallelogram in which P is the midpoint of DC and Q
is a point on AC such that CQ=1/4AC If PQ
produced meet BC att R, prove that R is the midpoint of BC

Aakash Sharma · Accepted Answer

Dear Student! Here is the answer to your query

Given : ABCD is a parallelogram and P is the mid point of DC Also, $CQ = \frac{1}{4} AC$ To prove : R is the mid point of BC Constriction : Join B and D and suppose it cut AC at O Proof : Now $OC = \frac{1}{2}$ AC (Diagonals of a parallelogram bisect each other) (1) and CD = $\frac{1}{4} AC$ (2) From (1) and (2) we get $CD= \frac{1}{2} OC$ In Î”DCO, P and Q are mid points of DC and OC respectively âˆ´ PQ || DO (mid point theorem) Also in Î”COB, Q is the mid point of OC and PQ || AB âˆ´ R is the mid point of BC (Converse of mid point theorem) Cheers!

ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ=1/4AC. If PQ produced meet BC att R, prove that R is the midpoint of BC.

ABCD is a parallelogram in which P is the midpoint of DC and Q is a point on AC such that CQ=¹/₄AC. If PQ produced meet BC att R, prove that R is the midpoint of BC.