Prove that median of a isoeceles trinangle is perpendicular to the unequal sides.
given:
ABC is an isosceles triangle with
AB = AC ---- by definition
If AD is the median to BC
BD = CD ---- given
AD = AD --- common side
therefore triangle ABD is congruent to triangle ACD (SSS)
Therefore angle ADB = angle ADC
but angle ADB + ADC = 180
so each angle = 90°