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Theorem 40

Theorem 40. By Jimmy Wymer. Theorem 40. If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary. Given: AB||CD Conclusion: <AEG=<CFE. Proof of Theorem 40.

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Theorem 40

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  1. Theorem 40 By Jimmy Wymer

  2. Theorem 40 If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary

  3. Given: AB||CD Conclusion: <AEG=<CFE

  4. Proof of Theorem 40 • Statements Reasons • AB||BC 1. Given • <AEG supp <GEB 2. Supp <s form a st < • <GEB=<CFH 3. || lines > alt. ext. <s = • <CFE supp <CFH 4. Supp <s form a st < • <AEG=<CFE 5. <s that are supp to = <s are =

  5. Proof #1 Statements Reasons 1. Fig ABCD AD||BC 1. Given 2. AB||DC 2. Given 3. Draw DE||AB 3. Parallel Postulate 4. Draw AE 4. 2 pts determine a seg 5. <DAE=<BEA 5. || lines => alt. Int. <s = 6. <BAE=<DEA 6. Same as 5 7. AE=AE 7. Reflexive 8. ΔAEB=ΔEAD 8. ASA 9. AB=DE 9. CPCTC 10. AB=DC 10. Given 11. DE=DC 11. Transitive 12. <DEC=<C 12. If Δ then Δ 13. <B=<DEC 13. || lines => corr. <s = 14. <B=<C 14. Transitive A D B C E Given: Fig ABCD AD||BC AB con DC AB||DC Conclusion: <B con <C

  6. Proof #2 A 1 Statements Reasons B 2 3 Given: A||B Conclusion: <1 con <3

  7. Proof #3 E D C 3 B F A 2 1 G H Given: <3 con <1 <2 con <3 Conclusion: EG||BH

  8. History • Was proposed by Euclid who lived from about 325 B.C. and died about 265 B.C. in Alexandria, Egypt • Is part of Proposition 28 in Book I of Euclid’s The Elements • Euclid proposed it around 300 B.C. • It is based on Proposition 15 in Book I • It is used in Proposition 7 in Book IV, Proposition 4 in Book VI, and it is used a few times in Book XI

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