1. Date:
5.6 Notes: Proving Lines Parallel
Lesson Objective: Recognize angle pairs that occur with parallel lines. Prove that 2 lines are parallel.
CCSS: G.CO.9, 12 Prove theorems about lines and angles. Make formal geometric constructions.

2. Lesson 1: Identify Parallel Lines
Draw a line segment x on one of your blue lines. Draw line segment y at a 40° angle on the left portion of the segment. Draw line segment z at a 40° angle to the right of y. x

3. Lesson 1: Identify Parallel Lines
Draw a line segment x on one of your blue lines. Draw line segment y at a 40° angle on the left portion of the segment. Draw line segment z at a 40° angle to the right of y.
y z
° ° x

4. Lesson 1: Identify Parallel Lines
What did you construct with line segments y and z? _______________________ How do we know they are ________________? Put the appropriate marks on lines y and z in red.
y z
° ° x

5. CONVERSE of Corresponding Angles Postulate:
If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
y| |z because: / 2 / 4
The other corresponding / s are:
y z
° ° x

6. x and y can also be proved to be parallel by:
Alternate Interior Angles CONVERSE:
Examples: / / __, / 3 / __
Consecutive Interior Angles CONVERSE:
Examples: m/ 2 + m/ __ = 180°
m/ __+ m/ __ = 180°
Alternate Exterior Angles CONVERSE:
Examples: / / __, / __ / __

7. Perpendicular Transversal Converse: If 2 lines are _|_ to the same line, then they are | |.

8. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8 b.
/ 3 / 11 c.
/ / 14 d.
/ 1 / 15 e.
m/ 8 + m/ 13 = 180° f.
/ 8 / 6

9. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11 c.
/ / 14 d.
/ 1 / 15 e.
m/ 8+m/ 13 = 180° f.
/ 8 / 6

10. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11
l| |m; Conv. Corr. / s c.
/ / 14 d.
/ 1 / 15 e.
m/ 8+m/ 13 = 180° f.
/ 8 / 6

11. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11
l| |m; Conv. Corr. / s c.
/ / 14
a| |b; Conv Alt Ext / s d.
/ 1 / 15 e.
m/ 8+m/ 13 = 180° f.
/ 8 / 6

12. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11
l| |m; Conv. Corr. / s c.
/ / 14
a| |b; Conv Alt Ext / s d.
/ 1 / 15
Not possible e.
m/ 8+m/ 13 = 180° f.
/ 8 / 6

13. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11
l| |m; Conv. Corr. / s c.
/ / 14
a| |b; Conv Alt Ext / s d.
/ 1 / 15
Not possible e.
m/ 8+m/ 13 = 180°
l| |m; Conv Consec Int / s f.
/ 8 / 6

14. Lesson 2: Identify Parallel Lines
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer. a.
/ 2 / 8
a| |b; Conv Alt Int / s b.
/ 3 / 11
l| |m; Conv. Corr. / s c.
/ / 14
a| |b; Conv Alt Ext / s d.
/ 1 / 15
Not possible e.
m/ 8+m/ 13 = 180°
l| |m; Conv Consec Int / s f.
/ 8 / 6

15. Lesson 3: Proving | | Lines
Find x so that l| |m in the following situa-tions. Name the postulate or theorem.
a. m/ 1 = (7x – 2)°
m/ 2 = (10 – 3x)°
b. m/ 1 = (4x – 23)°
m/ 3 = (2x + 17)°

16. Lesson 4:

17. 5.6: Do I Get It? Yes or No
Given the following information, determine which lines, if any, are parallel. State the pos-tulate or theorem that justifies your answer.
/ 1 / 6
/ 2 / 3
/ 3 / 5
m/ 4 + m/ 5 = 180

18. 5.6: Do I Get It? Continued
5. Find m/ MRQ so that a| |b. Show your work. Name the postulate or theorem that justifies your answer. Find m/ LRP.