1. 3-5 Proving Lines Parallelb c
Postulate 3.4: If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Line a would then be parallel to line b.

2. Construction
Using a compass and straightedge: follow the steps to draw a parallel line through a point not on a line. p. 172

3. Parallel Postulate
Postulate 3.5: If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

4. Example If m1 = 5x + 10 and m2 = 6x – 4, find x so that a || b.c 2 1
If m1 = 5x + 10 and m2 = 6x – 4, find x so that a || b.
They are corresponding angles so for the lines to be parallel they must be congruent.
1 2
m 1 = m 2
5x + 10 = 6x – 4
10 = x – 4
14 = x

5. Theorems
Theorem 3.5: If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles is congruent, then the two lines are parallel.
Theorem 3.6: If two lines are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the two lines are parallel.

6. More Theorems
Theorem 3.7: If two lines in a plane are cut by a transversal so that a pair of alternate interior angles is congruent, then the two lines are parallel.
Theorem 3.8: If two lines are perpendicular to the same line, then the two lines are parallel.

7. Example
Determine which lines are parallel, if any. What theorems were used? 68
112 E F D B C A

8. Example 9x = 10x – 8 -x = -8 x = 8 Are you done?b k f
10x - 8 9x
9x = 10x – 8
-x = -8
x = 8
Are you done?
No. You need to find the angle measure.
10(8) – 8 =
80 – 8 = 72
= 108
Find the value of x so that a || b. Then find kfb.
The angles are alternate exterior angles therefore they must be congruent.

9. Review Example 3 Proof p. 175
Do “Check your Progress” #4 p. 175.

10. Practice Try page 175-176 #1-7 before you begin your homework.
Homework #22 Practice Worksheet
p even, 29, 37-38