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Part 2: Proving and Applying Theorems About Angles

Part 2: Proving and Applying Theorems About Angles. Given : ∠A supp ∠B; ∠C supp ∠D; ∠B  ∠C Prove : ∠A  ∠D. ∠A supp ∠B; ∠C supp ∠D. Given. m ∠A + m ∠B = 180; m ∠C + m ∠D = 180. Def. of supp. ∠’s. m ∠A + m ∠B = m ∠C + m ∠D. . Substitution Prop. of =. ∠B  ∠C. Given. Def. of .

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Part 2: Proving and Applying Theorems About Angles

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  1. Part 2: Proving and Applying Theorems About Angles Geometry

  2. Geometry

  3. Given:∠A supp ∠B; ∠C supp ∠D; ∠B  ∠CProve: ∠A  ∠D ∠A supp ∠B; ∠C supp ∠D Given. m ∠A + m ∠B = 180; m ∠C + m ∠D = 180 Def. of supp. ∠’s m ∠A + m ∠B = m ∠C + m ∠D . Substitution Prop. of = ∠B  ∠C Given. Def. of  m ∠B = m ∠C m ∠A = m ∠ D Subtraction Prop. of = ∠A  ∠C Def. of  Geometry

  4. Vocabulary: Corollary corollary A _________ of a theorem is a theorem whose proof contains only a few additional statements in addition to the original proof. EXAMPLE: If two angles are supplements of the same angle, then the two angles are congruent. Geometry

  5. Geometry

  6. Given: ∠A comp . ∠B; ∠C comp. ∠D; ∠B  ∠CProve: ∠A  ∠D ∠A comp ∠B; ∠C comp ∠D Given. m ∠A + m ∠B = 90; m ∠C + m ∠D = 90 Def. of supp. ∠’s m ∠A + m ∠B = m ∠C + m ∠D Substitution Prop. of = ∠B  ∠C Given. m ∠B = m ∠C Def. of  m ∠A = m ∠ D (-) Prop. of = ∠A  ∠C Def. of  Geometry

  7. Given:∠ 1 and ∠ 3 are vertical angles1 3 2 Prove:∠ 1  ∠ 3 Geometry

  8. Given:∠ 1 and ∠ 3 are vertical anglesProve:∠ 1  ∠ 3 ∠ 1 and ∠ 3 are vertical angles Given. Def. of linear pair ∠ 1 and ∠2 are a linear pair ∠ 2 and ∠3 are a linear pair Def. of linear pair ∠1 supp ∠2; ∠3 supp ∠2 Linear pairs are supp. ∠ 1  ∠ 3 Supp. of same∠ Geometry

  9. Geometry

  10. Final Checks for Understanding In the following exercises, ∠ 1 and ∠ 3 are a linear pair, ∠ 1 and ∠ 4 are a linear pair, and ∠ 1 and ∠ 2 are vertical angles. Is the statement true? • ∠ 1  ∠ 3 b. ∠ 1  ∠ 2 • c. ∠ 1  ∠ 4 d. ∠ 3  ∠ 2 • e. ∠ 3  ∠ 4 f. m∠ 2 + m ∠ 3 = 180 Geometry

  11. Homework Assignment Pages 100-101: 10-18 all. Prove: 1932-35 all. Geometry

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