1. Warm Up
State the converse of each statement.
1. If a = b, then a + c = b + c.
2. If mA + mB = 90°, then A and B are complementary.
3. If AB + BC = AC, then A, B, and C are collinear.

2. Objective
Use the angles formed by a transversal to prove two lines are parallel.

4. Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
4  8

5. Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30

6. Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.
m1 = m3

7. The Converse of the Corresponding Angles Postulate is used to construct parallel lines. The Parallel Postulate guarantees that for any line ℓ, you can always construct a parallel line through a point that is not on ℓ.

9. Use the given information and the theorems you have learned to show that r || s.
4  8

10. Use the given information and the theorems you have learned to show that r || s.
m2 = (10x + 8)°,
m3 = (25x – 3)°, x = 5

11. Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.
m4 = m8

12. r Given: p || r , 1  3 Prove: ℓ || m l m p 1 2 3 Statements Reasons
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.

13. 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. s
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.

14. Name the postulate or theorem that proves p || r.
1. 4  5
2. 2  7
3. 3  7
4. 3 and 5 are supplementary.

15. Homework Pg#166 2, 6 – 18 evens 22,24,26,30, 32,34,46,48,50, 60