Transcript 3.1 IDENTIFY PAIRS OF LINES AND ANGLES

CHAPTER 3
Parallel and
Perpendicular Lines
3.1 IDENTIFY PAIRS OF LINES
AND ANGLES
Vocabulary
Types of
Lines
Definition / Characteristics
Symbol
Parallel lines
• never intersect
• are on the same plane
• have the same slope
Perpendicular
Lines
• cross to form 90 angles
• are on the same plane
┴
Skew lines
• never intersect
• do not lie on the same plane
n/a
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?
1)
2)
3)
4)
Line(s) parallel to line CD and containing point A
Line BA
Line(s) skew to line CD and containing point A
Line AH
Line(s) perpendicular to line CD and containing
point A
Line DA
Plane(s) parallel to plane EFG and containing
point A
Plane DCB
Postulates

A postulate is a true statement, which does
not require to be proved.
Parallel Postulate
There is exactly 1 line through a point parallel to
another line.
.
Perpendicular Postulate
There is exactly 1 line through a point perpendicular to
another line.

.
EXAMPLE 2
Identifying Parallel
and Perpendicular Lines
The given line markings show
how the roads are related to
one another.
1.
Name a pair of parallel lines.
2.
Name a pair of perpendicular
lines.
3.
Is line FE parallel to line AC ?
Explain.
Angle Pairs - review
(formed by the intersection of 2 lines)
Description/ Properties
Vertical Angles
angles that are opposite
one another

• These ’s are =
Linear pair
angles that are both
adjacent and supplementary
(next to)
( __ +___ = 180 )

Picture
Name 2 pairs of
vertical angles in
the picture above:
1 & 4
2 & 3
Name 4 sets of
linear pairs in the
picture above:
1 & 2
2 & 4
3 & 4
3 & 1
Transversal
a line that crosses 2 other lines
1 2 5 6
3 4 7 8
Angle Pairs
(formed by a transversal)
Angles are….
Corresponding
Angles
Alternate Interior
Angles
Alternate Exterior
Angles
Consecutive Interior
Angles
Angles are on the
______ side of
the transversal
in the same position
of each intersection
same
inside of the 2 lines
opposite
outside of the 2 lines
opposite
inside the 2 lines and
form a linear pair
same
Picture
Extra
Practice
Example 3
Identify all pairs of angles of the given type:
A. Corresponding
E.
Vertical Angles
1 & 5 2 & 6 3 & 7 4 & 8
1 & 4 2 & 3
A & E B & F D & H C & G
5 & 8 6 & 7
B. Alternate interior
4 & 5 2 & 7
D & E B & G
C. Alternate exterior
F.
Linear Pairs
1 & 8 3 & 6
1 & 2 2 & 4 3 & 4
A & H C & F
3 & 1 5 & 6 5 & 7
D. Consecutive interior
7 & 8 8 & 6
2 & 5 4 & 7
B & E D & G
GUIDED PRACTICE
Classify the pair of numbered angles in each picture
Alternate Exterior
angles
Corresponding angles
Alternate Interior
angles