1. Parallel and Perpendicular Lines
CHAPTER 3
Parallel and Perpendicular Lines

2. 3.1 IDENTIFY PAIRS OF LINES AND ANGLES

3. Vocabulary ┴ Types of Lines Symbol Definition / Characteristics
Parallel lines
Perpendicular
Lines
Skew lines
n/a
never intersect
are on the same plane
have the same slope
cross to form 90 angles ┴
are on the same plane
never intersect
do not lie on the same plane

4. EXAMPLE 1
Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?
Line(s) parallel to line CD and containing point A
Line(s) skew to line CD and containing point A
Line(s) perpendicular to line CD and containing point A
Plane(s) parallel to plane EFG and containing point A
Line BA
Line AH
Line DA
Plane DCB

5. Postulates
A postulate is a true statement, which does not require to be proved.

6. Parallel Postulate
There is exactly 1 line through a point parallel to
another line. .

7. Perpendicular Postulate
There is exactly 1 line through a point perpendicular to
another line. .

8. Identifying Parallel and Perpendicular Lines
EXAMPLE 2
Identifying Parallel and Perpendicular Lines
The given line markings show how the roads are related to one another.
Name a pair of parallel lines.
Name a pair of perpendicular lines.
Is line FE parallel to line AC ? Explain.

9. Description/ Properties
Angle Pairs - review
(formed by the intersection of 2 lines)
Description/ Properties
Picture
Vertical Angles
Linear pair
angles that are opposite
one another
Name 2 pairs of vertical angles in the picture above:
These ’s are =
Hyperlink
Name two pairs of vertical angles
How are vertical angle related?
Name all four adjacent angles
How are the adjacent angles related?
What is meant by supplementary angles?
Name four pairs of supplementary angles
What if l2 ┴ l2, what would the measurement be of each of the angles?
1 & 4 2 & 3
Name 4 sets of linear pairs in the picture above:
angles that are both
adjacent and supplementary
(next to)
( __ +___ = 180 )
1 & 2 2 & 4
3 & 4 3 & 1

10. Transversal
a line that crosses 2 other lines

11. (formed by a transversal)5 6 1 2 7 8
Angle Pairs 3 4
(formed by a transversal)
Angles are….
Angles are on the ______ side of the transversal
Picture
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Consecutive Interior Angles
in the same position of each intersection
same
opposite
inside of the 2 lines
outside of the 2 lines
opposite
inside the 2 lines and form a linear pair
same

12. Example 3 Identify all pairs of angles of the given type:
Extra Practice
Example 3
Identify all pairs of angles of the given type:
Corresponding E. Vertical Angles
Alternate interior
Alternate exterior F Linear Pairs
Consecutive interior
1 & 5 2 & 6 3 & 7 4 & 8 A & E B & F D & H C & G
1 & 4 2 & 3 5 & 8 6 & 7
4 & 5 2 & 7 D & E B & G
1 & 8 3 & 6 A & H C & F
1 & 2 2 & 4 3 & 4
3 & 1 5 & 6 5 & 7 7 & 8 8 & 6
2 & 5 4 & 7 B & E D & G

13. GUIDED PRACTICE Classify the pair of numbered angles in each picture
Alternate Exterior
angles
Alternate Interior
angles
Corresponding angles