Question

Q53. In AABC, P, Q and R are the mid-points of BC, CA
.
and AB respectively. PR and BQ meet in M and CR
1
and PQ meet in N. Prove that MN BC.​

Answer 1

Answer:

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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