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 Assertion and Reason are true but Reason is not the correct explanation of Assertion.
• C. The assertion is true but Reason is false.
• D. The 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 ${\Delta }^{\prime }s$ AEB and CED, we have
$\Rightarrow$ $\angle BAE=\angle DCE$ [Angles in the same segment are equal]
$\Rightarrow$ $\angle ABE=\angle CDE$ [Angles in the same segment are equal]
$\Rightarrow$ AB = CD [Given]
$\Delta AEB\cong \Delta CED$ [By A.S.A. congruence]
$\Rightarrow AE=CEandBE=DE$ [By c.p.c.t]