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Theorem 9.1 : Parallelograms on the same...

Theorem 9.1 : Parallelograms on the same base and between the same parallels are equal in area.

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Since opposite sides of parallelogram are equal,
`AD||BC` with transversal `AB`
`/_DAB=/_CBF` (Corresponding angles)
And, `AD=BC` (opposite sides of parallelogram are equal)
In `/_\AED` and `/_\BFC`
`/_DEA=/_CFE`
`/_DAB=/_CBF`
...
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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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