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