Given: AD is the perpendicular bisector of BC

Prove: Triangle ABC is Isosceles

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