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Understanding Flowchart and Paragraph Proofs in Geometry

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This lesson focuses on mastering flowchart and paragraph proofs in geometry. Students will explore how to complete sentences relating to angle relationships, such as congruence and supplementary angles. The lesson includes a warm-up activity, detailed examples of flowchart proofs, and the construction of two-column proofs. Students will practice ensuring the logical structure of their arguments through clear justifications for each step, enhancing their understanding of geometric concepts through visual representation and written explanations.

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Understanding Flowchart and Paragraph Proofs in Geometry

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  1. 2-7 Flowchart and Paragraph Proofs Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. Warm Up Complete each sentence. 1.If the measures of two angles are ? , then the angles are congruent. 2. If two angles form a ? , then they are supplementary. 3. If two angles are complementary to the same angle, then the two angles are ? . equal linear pair congruent

  3. A second style of proof is a flowchart 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 1: 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:

  5. Example 1 Continued Two-column proof: 1. 2 and 3 are comp. 1  3 1. Given 2. m2 + m3 = 90° 2. Def. of comp. s 3. m1 = m3 3. Def. of  s 4. m2 + m1 = 90° 4. Subst. 5. 2 and 1 are comp. 5. Def. of comp. s

  6. Check It Out! Example 1 Use the given flowchart proof to write a two-column proof. Given: RS = UV, ST = TU Prove: RT TV Flowchart proof:

  7. 5.RT TV Check It Out! Example 1 Continued 1.RS = UV, ST = TU 1. Given 2.RS + ST = TU + UV 2. Add. Prop. of = 3. Seg. Add. Post. 3.RS + ST = RT, TU + UV = TV 4.RT = TV 4. Subst. 5. Def. of  segs.

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