Given
Segment BD is the altitude of triangle ABC
Segment BD is the median of triangle ABC
Prove
Triangle ABC is isosceles
Given
Reflexive
Given
BD is the altitude
BD is congruent to
BD
BD is the median
Def of altitude
Def of median
<ADB & < BDC
Are perpendicular
AD is congruent
to DC
Def of perpendicular
M<ADB & m< BDC
= 90°
SAS
ADB is congruent
to CDB
CPCTC
AB is congruent to
CB
Def of isosceles
ABC is isosceles
Q.E.D.