1 / 11

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 .

ulfah
Download Presentation

Part 2: Proving and Applying Theorems About Angles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related