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Assertion (A) : In a trapezium ABCD, we ...

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.

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, Reason (R ) is true.
In trapezium ABCD, we find the `triangleABC and triangleABD` are on the same base and between the same parallels.
`therefore ar(triangleABC)=ar(triangleABD)`
`rArra r(triangleABC)-ar(triangleAOB)=ar(triangleABD)-ar(triangleAOB)`
`rArr ar(triangleBOC)=ar(triangleAOD).`
`therefore` Assertion (A) is true. And, clearly Reason (R ) gives Assertion (A). Hence, the correct answer is (a).
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Knowledge Check

  • In a trapezium ABCD, the diagonal AC and BD intersect each other at O such that OB:OD=3:1 then the ratio of areas of triangleAOB:triangleCOD is:

    A
    `3:1`
    B
    `1:4`
    C
    `9:1`
    D
    can't be determined

  • In the given figure, ABCD is a ||gm in which diagonals AC and BD intersect at O. If ar(||gm ABCD) is 52 cm^(2) then the ar(triangleAOB) =?

    A
    `26 cm^(2)`
    B
    `18.5 cm^(2)`
    C
    `39 cm^(2)`
    D
    `13 cm^(2)`

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