1. Proving Lines Parallel
Lesson 3-2:
Proving Lines Parallel
Teacher: Ms. Olifer

2. use a transversal and prove lines are parallel.
What are we learning?
SWBAT:
use a transversal and prove lines are parallel.

3. Proving Lines Parallel1 2 m
Postulate 3-2: Converse (Opposite) of Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the two lines are parallel. OR: If corresponding angles are congruent, then the lines are parallel.

4. Proving Lines Parallel
72°
We know these two lines are parallel!!
72°
108°
72°
If Alternate Interior Angles are congruent we can assume lines are parallel too!

5. Proving Lines Parallel1 4 2 m
Theorem 3-5: Converse of Alternate Interior Angles Theorem
If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.
OR: If alternate interior angles are congruent, then the lines are parallel.

6. Proof of Theorem 3-5 (C of AIAT)l 3 1 m 2
Statements
Reasons 1. 2. 3. 4.

7. Proving Lines Parallel
72°
We know these two lines are parallel!!
72°
108°
72°
If Same-Side Interior Angles are supplementary, we can assume lines are parallel too!!

8. Proving Lines Parallel1 4 2 m
Theorem 3-6: Converse of Same-Side Interior Angles Theorem
If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.
OR: If same side interior angles add up to 180 degrees, then the lines are parallel.

9. Proving Lines Parallel
108°
72°
We know these two lines are parallel!!
72°
108°
72°
108°
If Alternate Exterior Angles are congruent, we can assume lines are parallel!!!

10. Proving Lines Parallel1 b 3 2
Theorem 3-7: Converse of Alternate Exterior Angles Theorem
If two lines and a transversal intersects form alternate exterior angles that are congruent, then the two lines are parallel. OR: If alternate exterior angles are congruent, then the lines are parallel.

11. Proof of Theorem 3-7 (C of AEAT)1 4 b 2
Statements
Reasons 1. 2. 3. 4.

12. Proving Lines Parallel
108°
72°
We know these two lines are parallel!!
72°
108°
72°
108°
If Same-Side Exterior Angles are supplementary, we can assume lines are parallel!!!

13. Proving Lines Parallel1 b 3 2
Theorem 3-8: Converse of Same-Side Exterior Angles Theorem
If two lines and a transversal intersects form same-side exterior angles that are supplementary, then the two lines are parallel. OR: If same-side exterior angles add up to 180 degrees, then the lines are parallel.

14. Let’s Apply What We Have Learned….
Find the value of x for which l || m l
40° m
(2x + 6)°

15. You Try One!
Find the value of x for which a || b a
(7x - 8)° b
62°

16. Homework…
My momma always said, “Life was like a box of chocolates. You never know what you’re gonna get.”
-Forrest