The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

Assertion (A)

Reason (R)

In a trapezium ABCD we have AB ‖ DC and the diagonals AC and BD intersect at O.

Then, ar(∆AOD) = ar(∆BOC)

Triangles on the same base and between the same parallels are equal in areas.

Question

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct answer.

Assertion (A)

Reason (R)

In a trapezium ABCD we have AB ‖ DC and the diagonals AC and BD intersect at O.

Then, ar(∆AOD) = ar(∆BOC)

Triangles on the same base and between the same parallels are equal in areas.

Philoid · Accepted Answer

Assertion:

Here, Area (ΔABD) = Area(ΔABC) (∵ Triangles on same base and between same parallel lines) –1

Subtract Area (Δ AOB) on both sides of –1

Area (ΔABD) – Area (Δ AOB) = Area (ΔABC) – Area (Δ AOB)

Area (∆AOD) = Area (∆BOC)

∴ Both Assertion and Reason are true and Reason is a correct explanation of Assertion.