Question

p ,qand R the mid point of bc,ca and ab of a triangleabc. pr and bq meet at x cr and pq meet at y prove that xy=1/4 of bc

Answer 1

P,Q and R are respectively the mid points of sides BC,CA and AB of triangle ABC.PR and BQ meet atX. CR and PQ meet at Y. prove that XY=1/4BC.

Answer 2

Given

ABC is a Triangle.

P is the m.p of BC

Q is the m.p of CA

R is the m.p of AB

To prove

XY =  BC

Proof

In ΔABC

R is the midpoint of AB.

Q is the midpoint of AC.

∴ By Midpoint Theorem,

RQ║BC

RQ║BP → 1 [Parts of Parallel lines]

RQ =  BC → 2

Since P is the midpoint of BC,

RQ = BP → 3

From 1 and 3,

BPQR is a Parallelogram.

BQ and PR intersect at X

Similarly,

PCQR is a Parallelogram.

PQ and CR intersect at Y.

 X and Y are Midpoints of sides PR and PQ respectively.

In ΔPQR

X is the midpoint of PR

Y is the midpoint of PQ

∴ By Midpoint Theorem,

XY =  RQ

From 3,

XY =  +  BC

XY =  BC

Step-by-step explanation:

I hope it helps you