Question

If the altitude from one vertex of a triangle bisects the opposite side, prove that the triangle is isosceln.​

Answer 1

Answer:

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles. GIVEN : A A B C such that the altitude A D from A on the opposite side B C bisects B C i.e., B D=D. Cdot TO PROVE : A B=A C i.e. the triangle A B C is isosceles.

Answer 2

Answer:

if a line drawn from one vertex to the opposite side and it bisects it, it is called as median.

So, given that the line is altitude. And according to definition, line is also median. In isoceles triangle only, it is possible that median and altitude from same vertex to opposite side are same.

So, we can say that the triangle is isoceles.

HENCE PROVED.