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Triangles on the same base and between t...

Triangles on the same base and between the same parallel are equal in area.

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In `ABFD`
`DF||AB` and `BF||AD`
Thus, both pair of opposite sides are parallel.
Hence, `ABFD` id a parallelogram.
Similarly, we can prove that `ABCE` is a parallelogram with same base and between two parallels `AB` and `EF`.
`ar(ABFD)=ar(ABCE)`
In parallelogram `ABFD`,
...
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Knowledge Check

  • Assertion (A) : In a trapezium ABCD, we have AB ||DC and the diagonals AC and BD intersect at O. Then, ar(triangleAOD)= ar(triangleBOC) . Reason (R ) : Triangle on the same base between the same parallels are equal in area.

    A
    Both Assertion (A) and Reason (R ) are true and Reason (R ) is a correct explansion of Assertion (A).
    B
    Both Assertion (A) and Reason (R ) are true but Reason (R ) is not a correct explansion of Assertion (A).
    C
    Assertion (A) is true and Reason (R ) is false.
    D
    Assertion (A) is false and Reason (R ) is true.

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