4.3

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4.3 Prove Triangles Congruent by SSS
Geometry Ms. Rinaldi
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Side-Side-Side (SSS) Congruence Postulate
B

• If three sides of one triangle are congruent to
  three sides of a second triangle, then the two
  triangles are congruent.
• If Side
• Side
• Side
• Then

C
A
S
T
R
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EXAMPLE 1
Use the SSS Congruence Postulate
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
Given
Given
Reflexive Property
So, by the SSS Congruence Postulate,
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Use the SSS Congruence Postulate
EXAMPLE 2
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
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Use the SSS Congruence Postulate
EXAMPLE 3
Decide whether the congruence statement is true.
Explain your reasoning.
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Use the SSS Congruence Postulate
EXAMPLE 4
Decide whether the congruence statement is true.
Explain your reasoning.
A
B
C
D
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Use the SSS Congruence Postulate
EXAMPLE 5
Decide whether the congruence statement is true.
Explain your reasoning.
A
B
C
D
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Use the SSS Congruence Postulate
EXAMPLE 6
has vertices J(-3, -2), K(0, -2), and L(-3,
-8). has vertices R(10, 0), S(10, -3), and T(4,
0). Graph the triangles in the same coordinate
plane and show that they are congruent.
SOLUTION
Use the distance formula to find the lengths of
the diagonal segments.
LK TS 6.7 (By distance formula)
KJ SR 3. (By counting)
JL RT 6. (By counting)
Therefore, by SSS, the triangles are congruent.
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Use the SSS Congruence Postulate
EXAMPLE 7
has vertices P(-5, 4), Q(-1, 4), and R(-1,
1). has vertices A(2, 5), B(2, 1), and C(5,
1). Graph the triangles in the same coordinate
plane and show that they are congruent.
STEP 1 Graph
STEP 2 Use the distance formula to find the
lengths of the diagonal segments.
PR AC
PR _____ ______ (By ______________)
PQ _____ _____ (By_____________)
QR _____ _____ (By ____________)
Therefore, by ______, _________________________.