Question

If the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles.
If true then enter 1 else if False enter 0

Answer 1

Given, $△ABC$, AD bisects $\angle A$ and AD bisects BC.
To prove: ABC is an Isosceles triangle
In $△ABD$ and $△ACD$
$\angle DAB=\angle DAC$ (AD bisects $\angle A$)
$AD=AD$ (Common)
$BD=CD$ (AD bisects BC)
Thus, $△ABD\cong △ACD$ (SAS rule)
Thus, $AB=AC$ (By cpct)
hence, ABC is an Isosceles triangle.