Question

in the triangle ABC,D,E and F are respectively the mid point of BC ,CA and AB .if BE and of intersect at P and CF and DE intersect at Q then length of PQ is equal to ?​

Answer 1

Step-by-step explanation:

Given:△ABCwhereD,E,FarethemidpointsofthesidesBC,CAandABof△ABC.

ToProve:XY=

4

1

BC

Proof:

In△ABC,FandEarethemidpointsofABandACrespectively

∴FE∥BCandFE=

2

1

BC=BD(Thelinejoiningthemid−pointsoftwosidesofatriangleisparalleltothethirdsideandequaltohalfthelengthofthethirdside)

∴FE∥BDandFE=BD.

HenceBDEFisaparallelogramwhosediagonalsBEandDFintersecteachotheratX)

∴XisthemidpointofDF.

Similarly,YisthemidpointofDE.

Thus,in△DEF,XandYarethemidpointsofDFandDErespectively.

So,XY∥FEandXY=d

2

1

FE(MidpointTheorm)

=

2

1

×

2

1

BC=

4

1

BC

HenceProved