BD is congruent to DC

AD is the perpendicular bisector of BC

CPCTC

Reflexive

SAS (Side-Angle-Side)

AD is congruent to AD

All right angles are equal

angle ADB is congruent to angle ADC

AB is congruent to AC

Perpendicular lines form right angles

Given

angle ADB and angle ADC are right angles

Triangle ABD is congruent to Triangle ACD

Triangle ABC is Isosceles

Definition

Definition