Question

If the bisector of an angle of a triangle bisects the opposite side then the triangle is ______.

Options

• scalene

• equilateral

• isosceles

• right-angled

Answer 1

If the bisector of an angle of a triangle bisects the opposite side then the triangle is isosceles.

Explanation:

Let AD be the bisector of ∠A of ΔABC such that BD = DC.

Then, `(AB)/(AC) = (BD)/(DC) = 1`

⇒ AB = AC

So, the given triangle is isosceles.