Question

d is the midpoint of bc of triangle abc and e is the midpoint of ad. be produced meets ac at the point m . prove that be =3em

Answer 1

Given : d is the midpoint of bc of triangle abc and e is the midpoint of ad. be produced meets ac at the point m

To find :  Prove that be =3em

Solution:

Lets take a point F as mid point of  AC  

Now in Δ ADC

E & F are mid points of  AD  &   AC

=> EF ║ DC

& Δ AEF ≈ ΔADC

AE/AD = EF/DC

=> 1/2 =  EF/DC

=> EF/DC = 1/2

D is the mid point of BC

=> DC = BC/2

=> EF/ (BC/2) = 1/2

=> EF/BC = 1/4

now in  Δ MEF  &  Δ MBC

EF ║ BC

=> ME/MB = EF/BC

=> ME/MB = 1/4

=> MB = 4ME

=> BE = MB - ME = 4ME - ME = 3ME

=> BE = 3 EM

QED

Hence proved

Learn more:

D is the mid-point of side BC of triangle ABC and E is the mid point ...

https://brainly.in/question/7482552

in the joint figure P is a point on the side BC of triangle ABC such ...

https://brainly.in/question/7799775