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Mastering Triangle Congruence: ASA, AAS, HL Explained

Learn how to prove triangles congruent using ASA, AAS, and HL methods, with clear examples and helpful explanations. Explore included side concept and Third Angles Theorem in this comprehensive guide.

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Mastering Triangle Congruence: ASA, AAS, HL Explained

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  1. Objectives Apply ASA, AAS, and HL to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

  2. An ____________is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

  3. Example 1A: Applying ASA Congruence Determine if you can use ASA to prove the triangles congruent. Explain.

  4. Check It Out! Example 1B Determine if you can use ASA to prove NKL LMN. Explain.

  5. You can use the Third Angles Theorem to prove another congruence relationship based on ASA. This theorem is Angle-Angle-Side (AAS).

  6. Example 2A: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know.

  7. Example 2B: Applying HL Congruence

  8. Check It Out! Example 2C Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know.

  9. Example 3A: Using AAS to Prove Triangles Congruent Use AAS to prove the triangles congruent. Given:X  V, YZW  YWZ, XY  VY Prove: XYZ  VYW

  10. Check It Out! Example 3B Use AAS to prove the triangles congruent. Given:JL bisects KLM, K  M Prove:JKL  JML

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