1. Proving Lines Parallel
Section 3-5

2. 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.
If a + c = b + c, then a = b.
If A and  B are complementary, then mA + mB =90°.
If A, B, and C are collinear, then AB + BC = AC.

3. Write the converse of: “If 2 ║ lines are cut by a transversal, then corresponding angles are congruent.”

4. Example:
Use the Corresponding Angles Postulate and the given information to show that ℓ || m.
m1 = m3
1  3
ℓ || m

5. 4  8 Example: Use the given information to show that ℓ || m.

6. Example:
Use the given information to show that ℓ || m.
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
3  7
ℓ || m

9. Example: Determining Whether Lines are Parallel
Use the given information and the theorems you have learned to show that r || s.
4  8
4  8
r || s

10. Example : Proving Lines Parallel
Given: p || r , 1  3
Prove: ℓ || m

11. What lines are parallel?
Line BG bisects <ABF A B 45 D F 65 70 G H

12. Lesson Quiz: Part I
Name the postulate or theorem
that proves p || r.
1. 4  5
Conv. of Alt. Int. s Thm.
2. 2  7
Conv. of Alt. Ext. s Thm.
3. 3  7
Conv. of Corr. s Post.
4. 3 and 5 are supplementary.
Conv. of Same-Side Int. s Thm.

13. Lesson Quiz: Part II
Use the theorems and given
information to prove p || r.
5. m2 = (5x + 20)°, m 7 = (7x + 8)°, and x = 6
m2 = 5(6) + 20 = 50°
m7 = 7(6) + 8 = 50°
m2 = m7, so 2 ≅ 7
p || r by the Conv. of Alt. Ext. s Thm.