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Question

# This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: (a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A). (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation 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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Solution

## ANSWER: (a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.Given: A trapezium ABCD, AB∥DC.When two triangles are on the same base and between the same parallel lines then the area of two triangles is equal.Since, ΔADB and ΔABC are on the same base AB and between the same parallel lines AB and DC.Hence, ar(ΔADB)=ar(ΔABC).Now subtracting common area of the triangle ΔAOB from both the sides, we get,⇒ar(ΔADB)−ar(ΔAOB)=ar(ΔABC)−ar(ΔAOB)⇒ar(ΔAOD)=ar(ΔBOC)Hence, proved.

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