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Objective: To prove and apply theorems about angles.

Ch 2.5 Standard 2.0 : Students write geometric proofs. Standard 4 .0 : Students prove basic theorems involving congruence. Objective: To prove and apply theorems about angles. Theorems. Definition:.

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Objective: To prove and apply theorems about angles.

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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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