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.
• B. Both the assertion and reason are true, but reason is not the correct explanation for assertion.
• C. Assertion is true, but reason is false.
• D. Assertion is false, but reason is true.

Answer 1

The correct option is A

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

We have,



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