question_answer

Assertion (A): If the bisector of an angle of a triangle bisects the opposite side, then the triangle is isosceles.

Reason (R): The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

C) Assertion (A) is true but reason (R) is false.

D) Assertion (A) is false but reason (R) is true.

Correct Answer: A

Solution :

[a] Clearly, reason is true. Now, in \[\Delta ABC,\] the bisector AD of \[\angle A\] bisects the side BC.

( D is the mid-point of BC, \[\therefore \,\,\,\,BD=DC\])

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,AB=AC\]

Hence, the triangle ABC is isosceles.

\[\therefore \] Assertion: True and Reason : True and it is the correct explanation of assertion.