Given: 
In △ ABC, segment AC = segment BC and segment AB ≠ segment AC. segment AD is a median.

Prove: segment AD cannot be perpendicular to segment BC

Assume (for contradiction) that AD is perpendicular to BC

CD = BD                                  because AD is a median
AD is perpendicular to BC                by assumption (for contradiction)
Angle ADC = Angle ABD                    Because AD perp. to BC
AD = AD                                  symmetric property 
triangle ACD congruent to triangle ABD   SAS
AB = AC                                  C.P.C.T.
Contradiction to segment AB ≠ segment AC. 


Edwin