Question

Please solve this problem in a different sheet!! Thank you in advance for your help!!

Answer 1

нey

YᎾᏌᎡ solution is given below

__________________________________

Solution : since D and E are the mid points of the sides BC and AB respectively of triangle ABC

Therefore,

BE \\ BA

DE \\ FA............( 1 )

Since D and F are the mid points of the sides BC and AB respectively of ABC therefore,

DF \\ CA

DF \\ AE............(2)

From 1 and 2, we conclude that AFDE IS A PARALLELOGRAM.

similarly, BDEF is a parallelogram.

Now, in triangles DEF AND ABC, we have

< FDE = < A.
.................................. (opposite angles of \\ gm)

<DEF = <B


So, by AA similarity criterion, we have

Triangle DEF is similar to Triangle ABC

=>
$= ar(tringle \: def ) |ar \: (abc \: )| \: \\ \\ = {de}^{2} | {ab}^{2} | \\ \\ = ( {1 |2b| }^{2} | ) | {ab}^{2} | \\ \\ \\ = 1 |4|$


Hence ar (/DEF )/ Ar ( ABC)

=> 1:4

_________________________________

I hope it will help you

Thanks