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`XY` is a line parallel to side `BC` of a triangle `ABC`. If `B E ||A C` and `C F\ ||\ A B` meet `XY` at `E` and `F` respectively, show that `a r\ (A B E)\ =\ a r\ (A C F)`

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From diagram we can see that
`ar(EBCY)=ar(BXFC)`
`ar(/_AEB)=1/2ar(EBLY)`
`arBXFC=2ar(/_AFC)`
from both the equations
ar(/_AEB)=ar(/_AFC)
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NCERT ENGLISH-AREAS OF PARALLELOGRAMS AND TRIANGLES-Exercise 9.3
  1. Show that the diagonals of a parallelogram divide it into four triang...

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  2. In a triangle ABC, E is the mid-point of median AD. Show that a r\ (B...

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  3. In Fig.9.23, E is any point on median AD of a DeltaA B C. Show that a...

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  4. D and E are points on sides AB and AC respectively of Delta A B C su...

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  5. In Figure, diagonals AC and BD of quadrilateral ABCD intersect at O ...

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  6. D, E and F are respectively the mid-points of the sides BC, CA and AB...

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  7. In Fig. 9.24, ABC and ABD are two triangles on the same base AB. If l...

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  8. The side AB of a parallelogram ABCD is produced to any point P. A lin...

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  9. XY is a line parallel to side BC of a triangle ABC. If B E ||A C and ...

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  10. Diagonals A C\ a n d\ B D of a trapezium A B C D with A B||D C inte...

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  11. In Figure, A B C D E\ is a pentagon. A line through B parallel to A...

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  12. A villager Itwari has a plot of land of the shape of a quadrilateral...

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  13. ABCD is a trapezium with A B|| D C. A line parallel to AC intersects ...

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  14. In Figure, A P || B Q\ || C R. Prove that a r\ ( A Q C)=\ a r\ (P B R)

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  15. Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a ...

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  16. In Figure, a r\ ( D R C)=a r( D P C)a n d\ a r( B D P)=a r( A R C)dot ...

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