Prove the Converse of the Isosceles Triangle Theorem. It says that if two angles of a triangle are congruent, then the sides opposite those angles are also congruent.
The diagram shows
△
R
S
T
with
∠
R
∠
T
.
It also shows the altitude from
S
to a point
U
along
segment
R
T
.
Complete the proof that
segment
S
R
segment
S
T
.
Because 
segment
S
U
 is an altitude, 
∠
R
U
S
 and 
∠
T
U
S
 are  angles. And since  are congruent, 
∠
R
U
S
∠
T
U
S
. Also,  by the Reflexive Property of Congruence. So, by the Angle-Angle-Side Congruence Theorem, . Since  are congruent, 
segment
S
R
segment
S
T
.
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