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Understanding Triangle Congruence: ASA and AAS Postulates Explained

This educational material focuses on proving triangle congruence using the Angle-Side-Angle (ASA) Postulate and the Angle-Angle-Side (AAS) Theorem. It provides definitions, examples, and proofs to help you understand when two triangles can be considered congruent. The content includes key concepts, detailed explanations, and homework exercises for practice. Mastering these postulates is essential for students learning about triangle congruence in geometry.

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Understanding Triangle Congruence: ASA and AAS Postulates Explained

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Presentation Transcript

  1. Warm Up Can you determine that the triangles are congruent? Explain. A) B)

  2. Section 4 – 3 Triangle Congruence byASA and AAS Objective: To prove two triangles congruent using the ASA Postulate and the AAS Theorem

  3. Postulate 4 – 3Angle-Side-Angle (ASA) Postulate If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

  4. Example 1 Using ASA A) Name two triangles that are congruent by the ASA Postulate.

  5. B) Are these two triangles congruent? Why or Why not?

  6. Theorem 4 – 2Angle-Angle-Side (AAS) Theorem If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.

  7. Example 2 Using AAS A) Write a two-column proof to prove .

  8. B) Prove

  9. C) Given: Prove:

  10. Example 3 Using ASA and AAS What else must you know to prove the triangle congruent for the reason shown? A) B) C)

  11. Homework:Textbook Pg 197 – 198; #1 – 7, 9 – 12, 14 – 17

  12. Homework:Textbook Pg 197 – 198; #1 – 7, 9 – 12, 14 – 17

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