geometry help plz?

Question

In triangle ABC, AM is the median from A to BC, and angle AMC= 60.Prove that AB is not equal to AC. ( here we have to use indirect proof means we hav to start by assuming that AB is equal to AC and than we have to prove that AB is not equal to AC by using some contradiction)

any help would b graetly appreciated

Answer 1

BM = CM (definition of a median)
Assume AB = AC
AM = AM (reflexive)
Triangle ABM is congruent to triangle ACM (SSS)
Angle AMB = angle AMC (angle of congruent triangles)
Angle BMC = 180 degrees (straight line)
Angel AMB = angle AMC = 90 degrees
Contradicts angle AMC = 60
Therefore, AB is not = AC