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Proving Angle Theorems and Congruence through Two-Column Proofs

In this lesson, students will learn to prove and apply theorems related to angles, focusing on the understanding of two-column proofs. A theorem is a statement you can prove, and once proven, it serves as a foundation for future reasoning. Students will practice writing proofs with clear steps and reasoning. The lesson will include examples that illustrate how to prove angle relationships, particularly involving supplementary angles and congruence, ensuring students gain confidence in their proof-writing skills.

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Proving Angle Theorems and Congruence through Two-Column Proofs

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  1. Ch2.5Standard 2.0: Students write geometric proofs.Standard4.0:Students prove basic theorems involving congruence. Objective: To prove and apply theorems about angles.

  2. Theorems Definition: A theorem is any statement that you can prove. Once you have proven a theorem, you can use it as a reason in later proofs. Theorems:

  3. Two Column Proof Definition: In a two-column proof, you list the steps of the proof in the left column and the matching reason for each step in the right column. Step 1 is the hypothesis and the reason is Given. The last step is the conclusion of what you are proving. Before you start writing a proof, you should plan out your logic. Sample:

  4. Example 1 Given: 1 and 2 are supplementary, and 2 and 3 are supplementary. Prove: 1  3 1 and 2 are supp., and 2 and 3 are supp. m1 + m2 = m2 + m3 Subtr. Prop. of = 1  3

  5. Example 2 Given: 1 and 2 are supplementary, and 1  3 Prove: 3 and 2 are supplementary. 1 and 2 are supplementary. 1  3 Given m1 + m2 = 180° Def. of supplementary angles Def. ofcongruent angles m1 = m3 m3 + m2 = 180° Substitution Def. of supplementary angles 3 and 2 are supplementary

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