1. Parallel and Perpendicular Lines
Chapter 3
Parallel and Perpendicular Lines

2. Properties of Parallel Lines
Sec. 3-1
Properties of Parallel Lines
Objective: a) Identify Angles formed by Two Lines & a Transversal.
b) To Prove & Use Properties of Parallel Lines.

3. Parallel Lines – Two lines in the same plane which never intersect.
Symbol: “ // ”
Transversal – A line that intersects two // lines.
8 Special Angles are formed. t 1 2
Interior Portion of the // Lines m 3 4 5 6 n 7 8

4. Corresponding Angles Most Important Angle Relationship
Always Congruent
Cut the Transversal & lay the top part onto the bottom part. Overlapping Angles are Corresponding.
Corresponding Angles
1 & 5
2 & 6
3 & 7
4 & 8 1 2 3 4 5 6 7 8

5. P(3 – 1) Corresponding Angle Postulate
If a Transversal Intersects two // lines, then the corresponding angles are Congruent. 1 2 3 4 5 6 7 8

6. 4 Pairs of Vertical Angles Are Congruent 1  4 2  3
1   2  3
5  8 6  7 3 4 5 6 7 8
Special Interior Angles
3 & 6
4 & 5
Alternate Interior Angles
Are congruent
3 & 5
4 & 6
Same-Sided Interior Angles
Are Supplementary
(= 180)

7. Th (3-1) Alternate Interior Angle Theorem
If a Transversal intersects two // lines, then the alternate interior angles are congruent. 1 2 l
Given: l // m
Prove: 3  6 3 4 5 6 m 7 8
Statements
l // m
3  7
7  6
3  6
Reasons
Given
Corrsp. Angles are Congruent
Def. of Vertical Angles
Subs

8. Th (3-2) Same-Sided Interior Angle Theorem
If a Transversal intersects two // lines, then the same-sided interior angles are supplementary. 1 2 l 3 4
Given: l // m
Prove: 4 & 6 are Supplementary 5 6 m 7 8
Reasons
Given
 Add. Postulate
Corrsp. s are 
Subs
Def of Supplementary
Statements
l // m
m4 + m2 = 180
m2 = m6
m4 + m6 = 180
4 & 6 are Supplementary

9. Examples 1 & 2 Solve for the missing s Solve for x, then for each .
14x – 5 = 13x
-5 = -x
5 = x
5x – 20 +3x = 180
8x = 200
x = 25

10. Use what you have learned!
2. Solve for angles a, b, c if l//m
1. Find m2 if l//m. m c a b
42 l 1 2 65 40 m l
ma = 65 (Alt. Inter. )
mc = 40 (Alt. Inter. )
ma + mb + mc = 180
65 + mb + 40 = 180
m = 75
m1 = 42 (Corrsp. )
m1 + m2 = 180
42 + m2 = 180
m2 = 138

11. Solve for x and find the measure of each angle if l//m.
x + x +40 = 180
2x + 40 = 180
2x = 140
x = 70