Question

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Answer 1

Step-by-step explanation:Let XY intersect AB and BC at M and N respectively.

Given that XY is parallel to BC.

=En parallel to Bc (Parts of parallel lines are parallel)

Also given that BE parallel to AC

=BE parallel to CN.

In BCNE,both pair of opposite sides are parallel.

So, BCNE and triangle AEB lie on the same base BE and are between the same parallels BE and AC.

So,ar(triangle ABE)=1\2 ar(BCNE) ........(1)

Similarly, BCFM is a parallelogram and ar(triangle ACF)=1/2 ar (BCFM) .........(2)

Parallelogram BCNE and BCFM are on the same base and between the same parallels BC and EF.

THEREFORE, ar(BCNE)= ar(BCFM) ..........(3)

From (1),(2) and (3), we have,

ar(triangle ABE)=ar(triangle ACF) .............(hence proved)

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