Question

Assertion: If AD is a median of ∆ABC, then AB + AC > 2AD.
Reason: The angles opposite to equal sides of a triangle are equal.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

In triangle ABC, AD is a median.
We know that the sum of two sides of a triangle is greater than the third side.

$$\begin{gathered} AB+DB>AD....\left(i\right) \\ AC+DC>AD.........\left(ii\right) \\ \Rightarrow AB+AC+(DB+DC)>2AD \\ \Rightarrow AB+AC+BC>2AD \end{gathered}$$

In any triangle, angles opposite to equal sides are equal.
Clearly, the assertion and the reason are both true, but reason (R) does not give assertion (A).