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Using Theorems to Prove Triangle Congruency: ASA, SAS, and SSA Methods

This lesson focuses on the application of congruency theorems to prove triangle congruency using the ASA, SAS, and SSA rules. Students will learn to place congruency marks as evidence in their proofs, understand the correspondence of triangle parts through the Corresponding Parts of Congruent Shapes are Congruent (CPCSC) principle, and practice various examples, including alternate interior angles and midpoint definitions. The assignment includes exercises from the textbook to solidify understanding.

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Using Theorems to Prove Triangle Congruency: ASA, SAS, and SSA Methods

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  1. Week 5 Warm Up 11.14.11 Can the theorems be used to prove triangle congruency? 1) ASA 2) SAS 3) SSA

  2. Rule 1 Place congruency marks as you prove. B E Ex 1 C F A D ≅ Given: ∠A ≅∠D Given:

  3. CPCSC Corresponding Parts of Congruent Shapes are Congruent C B F G Ex 2 Given: ABCD ≅ EFGH H E A D Statement Reason ∠A ≅∠E CPCSC

  4. B C Ex 3 ∥ A D Given: ∥ Given: Prove: ∆ABD ≅ ∆CDB ∠ADB ≅ ∠CBD Alternate Interior Angles Theorem ∠ABD ≅ ∠CDB Alternate Interior Angles Theorem Reflexive Property of Congruence ≅ ∆ABD ≅ ∆CDB ASA

  5. Given: Given: A is midpoint of A is midpoint of Ex 4 M R A Prove: ∥ ∥ S T Given A is midpoint of and Definition of midpoint ≅ , ≅ ∠MAS ≅ ∠TAR Vertical Angles Theorem (2.6) SAS ( P19 ) ∆MAS ≅ ∆TAR CPCSC ∠SMA ≅ ∠RTA Alternate Interior Angles Converse ( T3.8 )

  6. Prove: ≅ Do: 1 N P L M Q Assignment: Textbook Page 232, 4 - 10 all and 14.

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