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Question

Assertion: If AB = CD, then BE = DE and AE = CE, where E is the point of intersection of AD and BC.

Reason: Angles in the same segment are equal.


Which of the following options is correct?


A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

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B

Both the assertion and reason are true, but reason is not the correct explanation for assertion.

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C

Assertion is true, but reason is false.

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D

Assertion is false, but reason is true.

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Solution

The correct option is A

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.


We have,



In Δs AEB and CED, since angles in the same segment are equal, we have
BAE=DCE and
ABE=CDE.
Also, AB = CD. [Given]
ΔAEBΔCED [By A.S.A. congruence]
AE=CE and BE=DE [By CPCT]
Thus, both reason and assertion are true, and reason is the correct explanation for assertion.


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