In the diagram below,
segment
S
V
bisects
∠
W
S
U
and
∠
X
V
T
.
Complete the proof that
△
S
W
V
△
S
U
V
.
segment
S
V
 bisects 
∠
X
V
T
. By the definition of an angle bisector, . Also, since vertical angles are congruent, . So, because the measures of congruent angles are equal, 
m
∠
S
V
X
m
∠
S
V
T
 and 
m
∠
W
V
X
m
∠
U
V
T
. 
By the , 
m
∠
W
V
S
m
∠
W
V
X
m
∠
S
V
X
. So, by substitution, 
m
∠
W
V
S
. It's also true that 
m
∠
U
V
S
m
∠
U
V
T
m
∠
S
V
T
 by the Additive Property of Angle Measure. So, by the , 
m
∠
W
V
S
m
∠
U
V
S
. Since angles with the same measure are congruent, 
∠
W
V
S
∠
U
V
S
. 
Now, since 
segment
S
V
 bisects 
∠
W
S
U
, . Also, 
segment
S
V
segment
S
V
 by the Reflexive Property of Congruence. So, by the  Congruence Theorem, 
△
S
W
V
△
S
U
V
. 
ref_doc_title.

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