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Triangle Congruence Proofs: ASA and AAS Theorems Explained

This lesson provides a comprehensive exploration of triangle congruence using the ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) postulates. We discuss specific examples and proofs, emphasizing congruent triangles, vertical angles, and the use of the Alternate Interior Angles Theorem. The lesson concludes with a guided plan for proof, illustrating how to substantiate congruence claims through rigorous reasoning. Perfect for students seeking to strengthen their understanding of triangle congruence theory and practice.

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Triangle Congruence Proofs: ASA and AAS Theorems Explained

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  1. The diagram shows NAD and FNCAGD. If F C, thenF C G. Therefore, FNI CAT GDO by ASA. Triangle Congruence by ASA and AAS LESSON 4-3 Additional Examples Suppose that F is congruent to C and I is not congruent to C. Name the triangles that are congruent by the ASA Postulate.

  2. It is given that A B and APBP. APX BPY by the Vertical Angles Theorem. Because two pairs of corresponding angles and their included sides are congruent, APXBPY by ASA. Triangle Congruence by ASA and AAS LESSON 4-3 Additional Examples Write a paragraph proof. Given: A B, APBP Prove: APXBPY

  3. Because AB || CD, BAC DCA by the Alternate Interior Angles Theorem. Then ABCCDA if a pair of corresponding sides are congruent. By the Reflexive Property, ACAC soABCCDA by AAS. Triangle Congruence by ASA and AAS LESSON 4-3 Additional Examples Write a Plan for Proof that uses AAS. Given: B D, AB || CD Prove: ABCCDA

  4. 1. B D, AB || CD1. Given 2. BAC DCA2. If lines are ||, then alternate interior angles are . 3. ACCA3. Reflexive Property of Congruence 4. ABCCDA4. AAS Theorem Triangle Congruence by ASA and AAS LESSON 4-3 Additional Examples Write a two-column proof that uses AAS. Given: B D, AB || CD Prove: ABCCDA Statements Reasons

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