Question

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

Answer 1

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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.
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Answer 2

Step-by-step explanation:

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

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