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Geometric Proof: Two-Column Proofs and Theorems Presentation

This lesson introduces writing two-column proofs to prove geometric theorems using deductive reasoning. It covers vocabulary such as theorems, postulates, and properties. Learners will practice justifying logical steps and applying definitions in examples. The presentation includes warm-up activities and quizzes to reinforce learning. With Holt McDougal Geometry content, students will grasp how to structure proofs based on given hypotheses. This engaging lesson fosters critical thinking skills in geometry.

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Geometric Proof: Two-Column Proofs and Theorems Presentation

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  1. 2-6 Geometric Proof Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry Holt Geometry

  2. Objectives: Write two-column proofs. Prove geometric theorems by using deductive reasoning (uses facts, rules, definitions to make conjectures from given situations) Vocabulary: Theorem – a statement that can be proven true. Two-column proof – format for proofs where the statements are listed on the left and the reasons are listed on the right.

  3. Definitions • Postulates • Properties • Theorems Conclusion Hypothesis When writing a proof, it is important to justify each logical step with a reason. You can use symbols and abbreviations, but they must be clear enough so that anyone who reads your proof will understand them.

  4. Example 1: Writing Justifications Write a justification for each step, given that A and Bare supplementary and mA = 45°. 1. A and Bare supplementary. mA = 45° Given information Def. of supp s 2. mA + mB= 180° Subst. Prop of = 3. 45° + mB= 180° Steps 1, 2 Subtr. Prop of = 4. mB= 135°

  5. A geometric proof begins with Given and Prove statements, which restate the hypothesis and conclusion of the conjecture. In a two-column proof, you list the steps of the proof in the left column. You write the matching reason for each step in the right column. Before you start writing a proof, you should plan out your logic. Sometimes you will be given a plan for a more challenging proof. This plan will detail the major steps of the proof for you.

  6. Check It Out! Example 2 Fill in the blanks to complete a two-column proof of one case of the Congruent Supplements Theorem. Given: 1 and 2 are supplementary, and 2 and 3 are supplementary. Prove: 1  3 Proof: • 1 and 2 are supp., and 2 and 3 are supp. b. m1 + m2 = m2 + m3 c. Subtr. Prop. of = d. 1  3

  7. Example 3: Writing a Two-Column Proof from a Plan Use the given plan to write a two-column proof. Given: 1 and 2 are supplementary, and 1  3 Prove: 3 and 2 are supplementary. Plan: Use the definitions of supplementary and congruent angles and substitution to show that m3 + m2 = 180°. By the definition of supplementary angles, 3 and 2 are supplementary.

  8. Example 3 Continued Given 1 and 2 are supplementary. 1  3 m1 + m2 = 180° Def. of supp. s m1 = m3 Def. of s Subst. m3 + m2 = 180° Def. of supp. s 3 and 2 are supplementary

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