Question

In triangle ABC, P, Q, R lie on sides BC, CA & AB. If BP = PC, PQ ║ AB & QR ║ BC, prove that RP ║ CA

Answer 1

Answer:

In a triangle line joining mid - point of two sides are parallel and half of third side

PQ∥AB

PQ=

2

1

AB→(i)

QR∥BC

QR=

2

1

BC→(ii)

PR∥AC

PQ=

2

1

AC→(iii)

fromequation(i)(ii)

two pairs are parallel so, BPQR is a parallelogram

BP=QR=

2

BC

→(iv)

In parallelogram diagonals bisects each other so

X is mid -point to PR. Similarly,

Y is mid- point on QP

InΔRPQ

XY=

2

1

QR

XY=

2

1

(

2

1

BC)

4

1

BC