Given: AD is the perpendicular bisector of BC

Prove: Triangle ABC is Isosceles

CPCTC
AD is congruent to AD
angle ADB is congruent to angle ADC
AB is congruent to AC
Reflexive
SAS (Side-Angle-Side)
Given
AD is the perpendicular bisector of BC
Perpendicular lines form right angles
All right angles are equal
BD is congruent to DC
angle ADB and angle ADC are right angles
Triangle ABD is congruent to Triangle ACD
Triangle ABC is Isosceles
Definition
Definition