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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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