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Write flowchart and paragraph proofs. Prove geometric theorems by using deductive reasoning.

Learn how to prove geometric theorems using deductive reasoning through flowchart and paragraph proofs. Practice examples included for better understanding and mastery of the concepts.

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Write flowchart and paragraph proofs. Prove geometric theorems by using deductive reasoning.

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  1. Objectives Write flowchart and paragraph proofs. Prove geometric theorems by using deductive reasoning.

  2. Vocabulary flowchart proof paragraph proof

  3. _________________- A second style of proof which uses boxes and arrows to show the structure of the proof. The justification for each step is written below the box.

  4. Example 1A: Reading a Flowchart Proof Use the given flowchart proof to write a two-column proof. Given: 2 and 3 are comp. 1  3 Prove: 2and 1are comp. Flowchart proof: Two-column proof: 1. 1. 2. 2. 3. 3. 4. 5. 4. 5.

  5. Example 1B Use the given flowchart proof to write a two-column proof. Given: RS = UV, ST = TU Prove: RT TV Flowchart proof: 1. 1. 2. 2. 3. 3. 4. 4. 5. 5..

  6. Example 2A: Writing a Flowchart Proof Use the given two-column proof to write a flowchart proof. Given: B is the midpoint of AC. Prove: 2AB = AC

  7. _________________– a style of proof that presents the steps of the proof and their matching reasons as sentences in a paragraph. Although this style of proof is less formal than a two-column proof, you still must include every step.

  8. Example 3: Reading a Paragraph Proof Use the given paragraph proof to write a two-column proof. Given: m1 + m2 = m4 Prove: m3 + m1 + m2 = 180° Paragraph Proof:It is given that m1 + m2 = m4. 3 and 4 are supplementary by the Linear Pair Theorem. So m3 + m4 = 180° by definition. By Substitution, m3 + m1 + m2 = 180°. Two-column proof: 1. 1. 2. 2. 3. 3. 4. 4.

  9. m3 + m4 = 90° 3 and 4 are comp. Example 4A: Writing a Paragraph Proof Use the given two-column proof to write a paragraph proof. Paragraph proof: Given: 1 and 2 are complementary Prove: 3 and 4 are complementary

  10. Example 4B Use the given two-column proof to write a paragraph proof. Given: 1  4 Prove: 2  3 Two-column proof: Paragraph proof:

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