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Congruent Triangles
Analyzing Congruence 4.3
Holt Geometry
Congruent Triangles
• Use the AAS Postulate to test for triangle congruence.
• Use the HL Postulate to test for right triangle congruence.
• Learn and apply the third angle theorem.
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Holt Geometry
Congruent Triangles
Vocabulary - AAS
B
B
AC is the non-included side in relation to
angles B and C.
AB is the non-included side in relation to
angles B and C.
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Holt Geometry
Congruent Triangles
Vocabulary – HL
(Right Triangles Only)
AC is a leg and AB is the hypotenuse.
CB is a leg and AB is the hypotenuse.
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Holt Geometry
Congruent Triangles
Third Angle Theorem
• Third Angle Theorem: If two angles of one
triangle are congruent to two angles of another
triangle, then the third angles are congruent.
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Holt Geometry
Congruent Triangles
Are the triangles are congruent by
SSS, SAS, ASA, AAS & HL
a. AAS
b. HL
c. SSS
d. HL
e. SAS
f.
HL
g. None
h. SAS
i. AAS
j.
SAS
k. AAS
l. None
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Holt Geometry
Congruent Triangles
Given: M  O
M  O
LNM  PNO
Prove: L  P
Vertical ’s Theorem
L  P
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Holt Geometry
Congruent Triangles
Summary
Name the Congruence Property
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Holt Geometry
Congruent Triangles
5 Congruence Properties
2 Imposters
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Holt Geometry
Congruent Triangles
Corresponding
Parts of
Congruent
Triangles are
Congruent
CPCTC
Once we know that two triangles are congruent,
we know that all corresponding sides and angles
are congruent!
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Holt Geometry
Congruent Triangles
Given:
Prove:
L
O
N
P
M
1.
1. Given
2. LNM  PNO
2. Vertical Angles Theorem
3. ΔLMN  ΔPON
3. SAS
4. L  P
4. CPCTC
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Holt Geometry
Congruent Triangles
Given:
Prove: Q  O
1.
1. Given
2.
2. Reflexive Property
3. ΔQNP  ΔOPN
4. Q  O
3. SSS
4. CPCTC
homework
Holt Geometry
Congruent Triangles
Assignment
Geometry:
4.3B
Section 10 – 19, 30 – 34
Holt Geometry