Question

Prove that triangle ABC is isosceles if any one of following holds (1) altitude AD bisects (2) median AD is perpendicular to the base BC.​

Answer 1

Answer:

in case 1

AD bisects base BC

so we get 2 triangles ADB

and ADC which are congruent

reason SSA or side side angle

meaning BD=CD

angle B= angle C

and AD is common side

Now

Since tri ABD and tri ACD are congruent we get AB=AC

so tri ABC ic isosceles tri.

Step-by-step explanation:

Case 2

If AD is perpendicular to BC in triangle ABC, it is

NOT

necessarily an isosceles tri because in any tri ABC ,

AD can be drawn perp to BC.