3.1: Lines and
Angles
1
Today’s Objectives

To identify relationships between figures in space

To identify angles formed by two lines and a transversal
Parallel Lines

Parallel lines are coplanar lines that do not intersect.

Arrows are used to indicate lines are parallel.

The symbol used for parallel lines is ||.
In the above figure, the arrows show that line AB is parallel to line CD.
With symbols we denote,
𝐴𝐵
𝐶𝐷 .
3
Skew Lines and Parallel Planes

Two lines are skew if they do not intersect and are not in the same plane (not coplanar).
Ex:

CG and EF
are skew.
All planes are either parallel or intersecting.
A

B
Parallel planes are two planes that do not intersect.
Ex: Plane ABC and Plane EFG
D
C
are parallel planes
E
H
F
G
4
Examples:
1.
2.
3.
4.
Name all segments that are parallel to
Name all segments that intersect
Name all segments that are skew to
Name all planes that are parallel to plane BCG.
A
Answers:
D
1. Segments BC, FG, & EH.
2. Segments DH, DC, AE & AB.
3. Segments CG, BF, FE, & GH.
4. Plane ADH.
H
B
C
E
F
5
G
Example:
1) What are the lines parallel to CD?
𝐴𝐵
𝐸𝐹
2) What lines are skew to CD?
𝐻𝐴
𝐺𝐵
𝐸𝐻
𝐹𝐺
3) Name the parallel plane to CDA.
𝐸𝐹𝐺
6
Transversal
Definition: A line that intersects two or more lines in a plane at
different points is called a transversal.
When a transversal t intersects line n and m, EIGHT angles are formed
t
m
Exterior angles: Outside the lines
Interior angles : Between the lines
n
7
Corresponding Angles
Corresponding Angles: Two angles, on the same side of the transversal, that
occupy corresponding positions, one interior and one exterior.
 2 and  6,  1 and  5,  3 and  7,  4 and
8
1
3
5
7
2
4
6
8
8
Alternate Angles
Alternate Interior Angles: Two angles that lie between the lines on opposite
sides of the transversal (but not a linear pair).
 3 and  6,
5
 4 and
Alternate Exterior Angles: Two angles that lie outside the lines on opposite
sides of the transversal.
1
3
5
7
2
 2 and  7,
8
4
6
8
9
 1 and 
Consecutive Angles
(aka Same-Side)
Consecutive Interior Angles: Two angles that lie between the lines, both on the
same side of the transversal.
3 and 5 ,
4 and 6
Consecutive Exterior Angles: Two angles that lie outside the lines, both on the
same side of the transversal.
1 and 7 ,
8
2 and
1
3
5
7
2
4
6
8
10
Vertical Angles & Linear Pair
Vertical Angles:
Two angles that are opposite angles.
Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Linear Pair:
Supplementary angles that form a straight line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
1
3
5
7
2
4
6
8
11
Example
List all pairs that fit the description
a. Corresponding
< 4 and < 2
< 3 and < 1
< 5 and < 7
b. Alternate Exterior
< 4 and < 8
< 1 and < 5
c. Alternate Interior
< 2 and < 6
< 3 and < 7
d. Consecutive Interior
< 3 and < 2
< 6 and < 7
< 6 and < 8
Example
Complete the statement with corresponding, alternate
exterior, alternate interior, or consecutive interior.
1. < 4 and < 8 are Alternate interior
2. < 2 and < 6 are Alternate exterior
3. < 1 and < 8 are Consecutive interior
4. < 7 and < 2 are Consecutive exterior
5. < 4 and < 6 are Corresponding
6. < 5 and < 7 are Vertical
Take Home Message

Parallel and skew lines

When a transversal intersects two other lines, 8
different angles are formed

Alternate vs Consecutive (same-side)

Interior vs. Exterior