4.4

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4.4 Prove Triangles Congruent by SAS

• Geometry
• Ms. Rinaldi

2
Included Angles

• The included angle is the angle between two sides.

3
Side-Angle-Side (SAS) Congruence Postulate
B

• If two sides and the included angle of one
  triangle are congruent to two sides and the
  included angle of a second triangle, then the two
  triangles are congruent.
• If Side
• Angle
• Side
• Then

C
A
S
T
R
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EXAMPLE 1
Use SAS
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(S) (A) (S)
So, by SAS,
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EXAMPLE 2
Use SAS
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
Although there are two pairs of congruent sides,
the congruent angles are not included (between)
the congruent sides. Therefore SAS does not apply
and the triangles are not congruent.
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EXAMPLE 3
Use SAS
Decide whether the congruence statement is true.
Explain your reasoning.
Hint This is possible! Do not forget the side
they both share!
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EXAMPLE 4
Use SAS
Decide whether the congruence statement is true.
Explain your reasoning.
Hint This is possible! You have the sides, you
only need a pair of congruent angles in between
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EXAMPLE 5
Use SAS
Decide whether the congruence statement is true.
Explain your reasoning.
Hint This is possible! Look for alternate
interior angles as well as a side that both
triangles share.
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EXAMPLE 6
Use SAS and properties of shapes
In the diagram, QS and RP pass through the center
M of the circle. What can you conclude about
MRS and MPQ?
SOLUTION
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EXAMPLE 7
Use SSS or SAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the SSS Congruence Postulate.
C
A
F
D
SOLUTION
To use SSS, you need to know that
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EXAMPLE 8
Use SSS or SAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the SAS Congruence Postulate.
C
A
F
D
SOLUTION
To use SAS, you need to know that
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EXAMPLE 9
Use SSS or SAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the SAS Congruence Postulate.
C
A
F
D