Question

XY is a line parallel to side BC of a triangle ABC. if BE parallel AC and CF parallel AB meet XY at E and F respectively.show that ar(∆ABE)=ar(∆ACF)​

Answer 1

Answer:

hi friend

here's your answer looking for

in a given figure,

AC is parallel to EB and EA is parallel to BC

Hence, ACBE is parallelogram.

and ,

AF is parallel to BC and AB is parallel to CF.

Hence, ABCF is parallelogram.

and , parallelogram ACBE and parallelogram ABCF is on same base BC and between same parallel lines EF and BC.

ar(ACBE)= ar(ABCF)

AND,

1/2×ar(ACBE)= 1/2×ar(ABCF)

ar(ABE) = ar(ACF)

Hence, proved.

I have attached the image to my answer.

Hope you are satisfied with my answer