Question

Let P,Q, R be the mid points of the sides BC, CA and AB of a given ∆ABC. Let BQ and PR
meet at X and CR and PQ meet at Y. Show that
a) XY║BC

Answer 1

Step-by-step explanation:n 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

InΔRPQ

XY=  

2

1

​  

QR

XY=  

2

1

​  

(  

2

1

​  

BC)

4

1

​  

BC

​  

 

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

$Hope this helps uh☺️❤️✌️$[tex][/tex]