1. 12. Conv. of corr. s post. 14. Both angles = 124°, Conv. of corr
12. Conv. of corr. s post Both angles = 124°, Conv. of corr. s post
16. Conv. of alt. int. s thm Conv. of same-side int. s thm
20. Both angles = 103°, Conv. of alt. int. s post
24. Conv. of corr. s post Conv. of alt. int. s thm
28. Conv. of alt. int. s thm L // M, Conv. of alt. int. s thm
32. L // N, Conv. of alt. ext. s thm L // N, Conv. of alt. int. s thm
40. Corresponding angles are same (123°) so plumb line and wall are parallel, which
makes the wall perfectly vertical.
46. Q // R, Conv. of alt. ext. s thm
47. None //
48. S // T, Conv. of corr. s post
49. Q // R, Conv. of alt. int. s thm
50. None //
51. S // T, Conv. of alt. ext. s thm
52. S // T, Conv. of same-side int. s thm
53. None //

2. Example 3A:
Given: p || r , 1  3
Prove: ℓ || m
Statements
Reasons
1. p || r
1. Given
2. 3  2
2. Alt. Ext. s Thm.
3. 1  3
3. Given
4. 1  2
4. Trans. Prop. of 
5. ℓ ||m
5. Conv. of Corr. s Post.

3. 8. Conv. of Same-Side Interior s Post.
Example 3B
Given: 1  4, 3 and 4 are supplementary.
Prove: ℓ || m
Statements
Reasons
1. 1  4
1. Given
2. m1 = m4
2. Def.  s
3. 3 and 4 are supp.
3. Given
4. m3 + m4 = 180
4. Def. of supp. angles
5. m3 + m1 = 180
5. Substitution
6. m2 = m3
6. Vert.s Thm.
7. m2 + m1 = 180
7. Substitution
8. ℓ || m
8. Conv. of Same-Side Interior s Post.