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andHL
HL
4-6
TriangleCongruence:
Congruence: ASA,
ASA, AAS,
AAS, and
4-7 Triangle
Section 4.7
Holt
HoltGeometry
McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Warm Up
1. What are sides AC and BC called? Side
AB?
2. Which side is in between A and C?
3. Given DEF and GHI, if D  G and
E  H, why is F  I?
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
An included side is the common side
of two consecutive angles in a polygon.
The following postulate uses the idea of
an included side.
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Name the included side between each pair of angles.
1. R and K
2. X and R
3. 8 and 9
4. 10 and 12
5. 5 and 1
6. 4 and 2
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Determine if you can use ASA to prove the
triangles congruent. Explain.
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Determine if you can use ASA to
prove NKL  LMN. Explain.
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
You can use the Third Angles Theorem to prove
another congruence relationship based on ASA. This
theorem is Angle-Angle-Side (AAS).
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
State the postulate that you would use to prove
the triangles congruent. Name the congruent
triangles.
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
State the postulate that you would use to prove
the triangles congruent. Name the congruent
triangles.
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Given: JL bisects KLM, K  M
Prove: JKL  JML
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
Holt McDougal Geometry
4-6 Triangle Congruence: ASA, AAS, and HL
What information is missing to say that:
a. ΔTUW  ΔQOS by SAS
Holt McDougal Geometry
b. ΔTUW  ΔQOS by
AAS
4-6 Triangle Congruence: ASA, AAS, and HL
Lesson Quiz: Part I
Identify the postulate or theorem that proves
the triangles congruent.
Holt McDougal Geometry