1. 3.2 Proving Lines Parallel

2. There are 4 ways to prove lines parallel
There are 4 ways to prove lines parallel. They are converses of the postulate and theorems from 3.3

3. Postulate 3-2:Converse of the Corresponding Angles Postulate
*If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. j 6 k
If j and k are cut by t and then 7 t

4. Theorem 3-3:Converse of the Alternate Interior Angles Theorem
*If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel. j
If j and k are cut by t and
then k 3 1 t

5. Theorem 3-4: Converse of the Same-Side (Consecutive) Interior Angles
*If two lines are cut by a transversal so that same-side (consecutive) interior angles are supplementary, then the lines are parallel. j
If j and k are cut by t and
are supplementary, then 3 k 1 t

6. *If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel. j
If j and k are cut by t and
are congruent, then 4 k 5 t

7. Ex 1. Find the value of x that makes j//k. Why?
*If two lines are cut by a transversal so that consecutive interior angles are supp., then the lines are parallel.

8. *If two angles form a linear pair, then they are supplementary.k j
2x+10 o b) o
120 o
120
*If two lines are cut by a transversal so that corr. angles are congruent, then the lines are parallel.
*If two angles form a linear pair, then they are supplementary.

9. k j
5x+10 o c) o 60
*If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

10. Ex 2. Is it possible to prove that lines a and b are parallel
Ex 2. Is it possible to prove that lines a and b are parallel? If so, state the postulate or theorem that you would use. a) t o 70 o 70 b a
Yes. If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

11. t b) a b
Yes. If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

12. c) t a b
No.

13. Theorem 3-5
If 2 lines are parallel to the same line, then they are parallel to each other. p q r
If p//q and q //r, then p // r.

14. Theorem 3-6
In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other. n m p
If and ,
then m // n.

15. Ex 1. State the postulate or theorem that allows you to conclude that a//b.
Given: a//c; and b//c b c
If 2 lines are parallel to the same line, then they are parallel to each other.

16. b) Given: c b
In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other. a

17. b
c) Given: a 2 1
If 2 lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

18. Ex 2. Determine which lines, if any, must be //. Explain.
l // m n a) p o
If two angles form a linear pair, then the angles are supplementary.
113 o 66 o 67 l 1 o 67 m
If two lines are cut by a trans. so that corr. angles are congruent, then the lines are //.