Question

Assertion: If AD is a median of ∆ABC, then AB + AC > 2AD.

Reason: In a triangle the sum of two sides is greater than the third side.
(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

(a) The Assertion and Reason are both true and the Reason is a correct explanation of the Assertion.
So, the Reason is obviously true. Let us consider the Assertion.

In triangle ABD, $AB+BD>AD$.

Similarly, in triangle ADC, $AC+CD>AD$.

Adding the above two expressions, we get:
$$\begin{gathered} AB+AC+BD+CD>AD+AD \\ \Rightarrow AB+AC+BD+DC>2AD \\ \Rightarrow AB+AC+BC>2AD \end{gathered}$$

Thus, the Assertion is true and the Reason is true. The Reason is an explanation of the Assertion.