In the diagram below,
segment
V
W
segment
X
S
and
segment
U
V
segment
T
S
.
Also,
segment
U
T
segment
W
X
.
Complete the proof that
∠
V
∠
S
.
In the diagram,
segment
V
W
segment
X
S
and
segment
U
V
segment
T
S
.
Also,
segment
U
T
segment
W
X
.
Because congruent segments have the same length,
U
T
W
X
.
By the Additive Property of Length, 
U
W
U
T
T
W
. So, by substitution, 
U
W
. It's also true that 
T
X
 by the Additive Property of Length. By the Transitive Property of Equality, . Since  are congruent, 
segment
U
W
segment
T
X
. So, by the Side-Side-Side Congruence Theorem, 
△
U
V
W
. Finally, because corresponding parts of congruent triangles are congruent, 
∠
V
∠
S
.
ref_doc_title.

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Skill IconL.6SSS, SAS, ASA, and AAS Theorems
Skill IconL.8Proving triangles congruent by SSS, SAS, ASA, and AAS
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Skill IconM.5Similar triangles and indirect measurement
Skill IconM.13Similarity and altitudes in right triangles
Skill IconM.15Prove similarity statements
Skill IconM.17Proofs involving similarity in right triangles