This document discusses different postulates and theorems for proving when two lines are parallel. It provides five statements for when lines are parallel based on angles formed when cut by a transversal, such as if corresponding angles are congruent. It then gives examples of applying these rules to determine if lines are parallel. The document emphasizes remembering the angle relationships that are formed when parallel lines are cut by a transversal and provides practice problems for readers to determine if lines are parallel.

1.  Starter 
1. 3.
2. 4.

2. Lesson 2-5: Proving Lines Parallel 2
Proving Lines Parallel - Postulates & Theorems
• If two lines are cut by a transversal and corresponding angles are
congruent, then the lines are parallel.
DC
BA

3. Lesson 2-5: Proving Lines Parallel 3
Proving Lines Parallel - Postulates &Theorems
• If two lines are cut by a transversal and alternate interior angles are
congruent, then the lines are parallel.
DC
BA

4. Lesson 2-5: Proving Lines Parallel 4
Proving Lines Parallel - Postulates &Theorems
• If two lines are cut by a transversal and alternate exterior angles are
congruent, then the lines are parallel.
DC
BA

5. Lesson 2-5: Proving Lines Parallel 5
Proving Lines Parallel - Postulates &Theorems
• If two lines are cut by a transversal and consecutive (same-side) interior
angles are supplementary, then the lines are parallel.
DC
BA

6. Lesson 2-5: Proving Lines Parallel 6
Proving Lines Parallel - Postulates &Theorems
• If two lines are cut by a transversal and consecutive (same-side) exterior
angles are supplementary, then the lines are parallel.
DC
BA

7. Lesson 2-5: Proving Lines Parallel 7
Examples: Proving Lines Parallel
• Find the value of x which will make lines a and lines b parallel.
2.
80
2x
b
a1.
60
3x
b
a
3.
70
(x-20)
b
a 4.
60
3x
b
a

8. Remember:
• If a transversal intersect two PARALLEL LINES then…
•Same Side Interior angles are __________
•Same Side Exterior angles are __________
•Alternate Interior angles are _____________
•Alternate Exterior angles are ____________
•Corresponding angles are ___________

9. Converse is also true.
• If Same side Interior Angles are supp then
_________________________________
• If Same Side Exterior Angles are supp then
__________________________________
• If Alternate Interior Angles are Congruent then
______________________________
• If Alternate Exterior Angles are Congruent then
______________________________
• If Corresponding Angles are congruent then
____________________________________

10. Example p125; #1
Based on the markings, which lines are parallel?

11. You Try: p125; #2 & 3
Which lines are Parallel?
L

12. Tricky? Use Colored Pencils!! P125; # 4 - 15

13. Theorem – Statement that CAN be proven!
• Theorem 3.5
• If two lines are parallel to the same line, then they are parallel to each other.
• Theorem 3.6
• If two lines are perpendicular to the same line, then they are parallel to each other.

14. Use Algebra. P126; #21

15. You Try #20 & 22