1. 3.3 Proving Lines Parallel
Geometry
3.3 Proving Lines Parallel

2. Postulate From yesterday :~
From yesterday :
If two // lines are cut by a transversal, then corresponding angles are congruent.
// Lines => corr. <‘s = 1 2 3 4 5 6 7 8 ~
<1 = <5

3. Postulate Today, we learn its converse :
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. ~
corr. <‘s = => // Lines 1 2 3 4 5 6 7 8 ~ //
If <1 = <5, then lines are

4. Theorem From yesterday:~
From yesterday:
If two // lines are cut by a transversal, then alternate interior angles are congruent.
// Lines => alt int <‘s = 1 2 3 4 5 6 7 8 ~
Example: <3 = <6

5. Theorem Today, we learn its converse :
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. ~
alt int <‘s = => // Lines 1 2 3 4 5 6 7 8 ~ //
If <3 = <6, then lines are

6. Theorem From yesterday:
If two // lines are cut by a transversal, then same side interior angles are supplementary.
// Lines => SS Int <‘s supp 1 2 3 4 5 6 7 8
Example: <4 is supp to <6

7. Theorem Today, we learn its converse :
If two lines are cut by a transversal and same side interior angles are supplementary, then the lines are parallel .
SS Int <‘s supp => // Lines 1 2 3 4 5 6 7 8
If <4 is supp to <6, then the lines are //

8. Theorem From yesterday:
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

9. Theorem t Today, we learn its converse:
In a plane two lines perpendicular to the same line are parallel. t k l
If k and l are both to t then the lines are //

10. 3 More Quick Theorems
Theorem: Through a point outside a line, there is exactly one line parallel to the given line.
Theorem: Through a point outside a line, there is exactly one line perpendicular to the given line.
Theorem: Two lines parallel to a third line are parallel to each other. . .

11. Which segments are parallel ?…
Are WI and AN parallel?
No, because <WIL and <ANI
are not congruent
61 ≠ 62 22 23 61 62 L I N E
Are HI and TN parallel?
Yes, because <WIL and <ANI
are congruent
= 84
= 84

12. In Summary (the key ideas)………

13. 5 Ways to Prove 2 Lines Parallel~
Show that a pair of Corr. <‘s are =
√ √ √ √ √ Alt. Int. <‘s are =
√ √ √ √ √ S-S Int. <‘s are supp
Show that 2 lines are to a 3rd line
√ √ √ √ √ to a 3rd line ~

14. Turn to pg. 87
Let’s do #19 and # 28 from your homework together

15. Homework
pg. 87 # 1-27 odd