p. 76-7 #1-6, 12-17, 23-27 odd, 30-39 all 1. alt int 2. Corr   1. alt int 2. Corr 3. s-s int 4. Alt int 5. Corr 6. corr 12. Corr 13. Corr 14. Alt Int 15. s-s int 16. s-s int 17. corr

p. 76-7 #1-6, 12-17, 23-27 odd, 30-39 all 23. 𝐹𝐿 𝐵𝐻 𝐸𝐾 𝐷𝐽 𝐶𝐼   23. 𝐹𝐿 𝐵𝐻 𝐸𝐾 𝐷𝐽 𝐶𝐼 24. ED KJ GH 25. fl, eK, DJ, CI, GL, LK, JI, IH 26. Plane GHIJKL and Plane CDJI 27. ABC BCH CDJ EDJ

p. 76-7 #1-6, 12-17, 23-27 odd, 30-39 all 30. Always 31. Sometimes   30. Always 31. Sometimes 32. Never 33. Always 34. Sometimes 35. Sometimes 36. Sometimes 37. Always 38. Sometimes 39. Sometimes

Chapter 3 Section 2

Section 3.2 Theorem 3.2 If two parallel lines are cut by a transversal, then alternate interior angles are congruent Theorem 3.3 If two parallel lines are cut by a transversal, then same side interior angles are supplementary Theorem 3.4 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

Theorem 3.2 If two parallel lines are cut by a transversal, then alternate interior angles are congruent 𝐺𝑖𝑣𝑒𝑛:𝑘∥𝑛;𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑎𝑙 𝑡 𝑐𝑢𝑡𝑠 𝑘 𝑎𝑛𝑑 𝑛 𝑃𝑟𝑜𝑣𝑒: ∠1 ≅ ∠2 Statement Reasons 1. 𝑘∥𝑛 1. 𝐺𝑖𝑣𝑒𝑛 2. 𝑉𝑒𝑟𝑡 ∠𝑠 𝑎𝑟𝑒 ≅ 2. ∠1≅∠3 3. 𝐼𝑓 𝑡𝑤𝑜 ∥𝑙𝑖𝑛𝑒𝑠 𝑎𝑟𝑒 𝑐𝑢𝑡 𝑏𝑦 𝑎 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙, 𝑡ℎ𝑒𝑛 𝑐𝑜𝑟𝑟 ∠𝑠 𝑎𝑟𝑒 ≅ 3. ∠3≅∠2 4. 𝑇𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑣𝑒 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 4. ∠1≅∠2

Theorem 3.3 If two parallel lines are cut by a transversal, then same side interior angles are supplementary 𝐺𝑖𝑣𝑒𝑛:𝑘∥𝑛;𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑎𝑙 𝑡 𝑐𝑢𝑡𝑠 𝑘 𝑎𝑛𝑑 𝑛 𝑃𝑟𝑜𝑣𝑒: ∠1 𝑖𝑠 𝑠𝑢𝑝𝑝𝑙𝑒𝑚𝑒𝑛𝑡𝑎𝑟𝑦 𝑡𝑜 ∠4 Statement Reasons 1. 𝑘∥𝑛 1. 𝐺𝑖𝑣𝑒𝑛 2. ∠𝐴𝑑𝑑 𝑃𝑜𝑠𝑡 2. ∠2+∠4=180 3. ∠2 𝑖𝑠 𝑠𝑢𝑝𝑝 𝑡𝑜 ∠4 3. 𝐼𝑓 𝑡𝑤𝑜 ∠𝑠 ℎ𝑎𝑣𝑒 𝑎 𝑠𝑢𝑚 𝑜𝑓 180, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 ∠𝑠 𝑎𝑟𝑒 𝑠𝑢𝑝𝑝 4. 𝐼𝑓 2 ∥ 𝑙𝑖𝑛𝑒𝑠 𝑎𝑟𝑒 𝑐𝑢𝑡 𝑏𝑦 𝑎 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑡ℎ𝑒 𝑎𝑙𝑡 𝑖𝑛𝑡 ∠𝑎𝑟𝑒≅ 4. ∠1≅∠2 5. ∠1 𝑖𝑠 𝑠𝑢𝑝𝑝 𝑡𝑜 ∠4 5. 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛

Theorem 3.4 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also. 𝐺𝑖𝑣𝑒𝑛:𝑙∥𝑛;𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑎𝑙 𝑡 𝑐𝑢𝑡𝑠 𝑘 𝑎𝑛𝑑 𝑛;𝑡⊥𝑙 𝑃𝑟𝑜𝑣𝑒:𝑡⊥𝑛 Statement Reasons 1. 𝑡⊥𝑙;𝑡⊥𝑛;𝑡𝑟𝑎𝑛𝑠 𝑡 𝑐𝑢𝑡𝑠 𝑘 𝑎𝑛𝑑 𝑛 1. 𝐺𝑖𝑣𝑒𝑛 2. 𝐼𝑓 𝑡𝑤𝑜 𝑙𝑖𝑛𝑒𝑠 𝑎𝑟𝑒⊥, 𝑡ℎ𝑒𝑦 𝑓𝑜𝑟𝑚 𝑎 90 ∠ 2. ∠1=90 3. ∠2≅∠1 3. 𝐼𝑓 𝑎 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙 𝑐𝑢𝑡𝑠 𝑡𝑤𝑜∥𝑙𝑖𝑛𝑒𝑠, 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑐𝑜𝑟𝑟 ∠𝑠 𝑎𝑟𝑒≅ 4. 𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑖𝑜𝑛 4. ∠2=90 5. 𝑡⊥𝑛 5. 𝑖𝑓 2 𝑙𝑖𝑛𝑒𝑠 𝑓𝑜𝑟 𝑎 90∠ 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑙𝑖𝑛𝑒𝑠 𝑎𝑟𝑒 ⊥

2. If 2 ll lines are cut by a transversal, then the Corr angles are congruent 3. If 2 ll lines are cut by a transversal, then the Alt Int angles are cong 4. If 2 ll lines are cut by a transversal then s-s-int angles are sup 5. If 2 ll lines are cut by a transversal, then corr angles are cong 6. If 2 ll lines are cut by a transversal, then alt int angles are cong 7. Vertical angles are congruent 8. If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also 9. If 2 ll lines are cut by a transversal then s-s int angles are supp 10. 130,50 11. x, 180-x 12. 60 13. 100

Homework: Pages 80-82 Written Exercises 1-11 odd, 15, 19, BRING COMPASS TO NEXT CLASS