Lesson on Parallel Lines & Transversals

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