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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 Assertion and Reason are true but Reason is not the correct explanation of Assertion.

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C

The assertion is true but Reason is false.

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D

The assertion is false but Reason is true.

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Solution

The correct option is D

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


We have,



In Δs AEB and CED, we have
BAE=DCE [Angles in the same segment are equal]
ABE=CDE [Angles in the same segment are equal]
AB = CD [Given]
ΔAEBΔCED  [By A.S.A. congruence]
AE=CE and BE=DE [By c.p.c.t]


Mathematics

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