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Proving Triangles Congruent by SAS
Name
You can also prove two triangles congruent by using relationships between a pair of
corresponding sides and an included angle.
The word included refers to the angles and sides of a triangle as shown below.
 A is the included angle of sides __________ and __________.
 B is the included angle of sides __________ and __________.
C is the included angle of sides __________ and __________.
BC is the included side of angles __________ and __________.
AC is the included side of angles __________ and __________.
AB is the included side of angles __________ and __________.
Side-Angle-Side (SAS) Postulate
If two sides and the included angle of one triangle are congruent to two
corresponding sides and the included angle of a second triangle, then the two
triangles are congruent.
1. Given: X is the midpoint of BD ,
X is the midpoint of AC
Prove: DXC  BXA
Proof:
Statements
D
A
X
C
B
Reasons
S
2. Given: 1 and 2 are right angles,
1
ST  PT
T
2
Prove: STR  PTR
Proof:
Statements
Reasons P
R
What other information do you need to prove DEF  FGD ? Explain.
What other information do you need to prove LEB  BNL ? Explain.
Would you use SSS or SAS to prove the triangles congruent? If there is not
enough information, to prove the triangles congruent by SSS or SAS, write not
enough information. Explain your answer.
a)
b)
c)
d)
Reflection:
1. Can both SSS and SAS Postulate be used to prove the triangles congruent?
Explain?