3-1 Lines and Angles
Today you will learn to
identify relationships
between figures in
space.
What would you call two lines
which do not intersect?
Parallel
B
A
D
C
A solid arrow placed
on two lines of a
diagram indicate the
lines are parallel.
The symbol || is used to
indicate parallel lines.
AB || CD
A slash through the parallel symbol || indicates the
lines are not parallel.
B
AB || CD
A
D
C
Skew Lines
Two lines are skew if they are not in the
same plane and do not intersect.
AB does not intersect
CD .
A
C
B
D
Since the lines are not
in the same plane,
they are skew lines.
Vocabulary




Parallel lines are coplanar lines that do not
intersect.
Lines in different planes that do not intersect
are skew.
Parallel planes are planes that do not
intersect.
Perpendicular lines – lines that intersect and
form right angles
Identifying Types of Lines and Planes
Identify each of the following.
A. a pair of parallel segments
LM ||QR
B. a pair of skew segments
KN and PQ
C. a pair of perpendicular segments
NS  SP
D. a pair of parallel planes
plane NMR || plane KLQ
Identify each of the following.
a. a pair of parallel segments
BF || EJ
b. a pair of skew segments
BF and DE are skew.
c. a pair of perpendicular segments
BF  FJ
d. a pair of parallel planes
plane FJH || plane BCD
Identifying relationships in space

a.
b.
c.
d.
Think of each segment in
the diagram. Which
appear to fit the
description?
Parallel to AB and contains
D
Perpendicular to AB and
contains D
Skew to AB and contains
D
Name the plane(s) that
contains D and appear to
be parallel to plane ABE
B
C
D
A
F
E
G
H
Parallel Postulate

If there is a line and a point not on the line,
then there is exactly one line through the
point parallel to the given line.
P
l
Perpendicular Postulate

If there is a line and a point not on the line,
then there is exactly one line through the
given point perpendicular to the given line.
P
l
Exit Ticket
List the plane(s)
parallel to plane
CDE.
Homework: WB p. 59 #1-15
3-1 Lines and Angles
Today you will learn to
identify angles formed
by parallel lines and a
transversal.
Transversals

If you have 2
coplanar lines that
are intersected by a
third (called a
transversal), special
angle pairs are
formed.
Transversal
Interior Angles

Angles between the
two lines are interior
angles.
Exterior Angles

Angles outside of
the two lines are
exterior angles.
Same Side Angles

Angles on the same
side of the transversal
are same side angles.
Alternate Angles

Angles on the opposite
side of the transversal
are alternate angles.
Combined Angles

The types of angles
mentioned previously
are only useful to us in
certain combinations:
–
–
–
–
Alternate interior
Same side interior
Alternate exterior
Same side exterior
(rarely used)
Corresponding Angles


If two angles occupy
the same relative
position at each of the
points of intersection,
they are corresponding
angles.
Which pairs of angles
are corresponding?
1
2
3
4
5
6
7
8
Parallel Lines & Transversals

Parallel lines are lines
in the same plane that
do not intersect.
a
a b

When a transversal
intersects parallel
lines, the special
angles pairs take on
certain properties.
b

These arrows are how
parallel lines are
marked on a diagram.
Parallel Lines Cut by a Transversal


Get into pairs. On a sheet of paper, draw two
parallel lines (either both horizontal or vertical).
Now use your ruler to draw a transversal that
intersects both parallel lines.
1 2
4 3
5 6
8 7
Label these pairs of angles:
1&5
4&6
2&8
Parallel Postulate
(Remember, a postulate is
something we accept as true
without proof.)
 If parallel lines are
intersected by a transversal,
then the corresponding
angles are congruent.
 In other words, if a ll b, then
1  2.
a
1
2
b
Parallel Lines & Transversal
Parallel lines and transversals
form special angles:
 Corresponding angles are
congruent
 Alternate interior angles are
congruent
 Same side interior angles
are supplementary
 Alternate exterior angles
are congruent
A Special Case


If there are a pair of
parallel lines, and a
transversal is
perpendicular to one of
them, then it is
perpendicular to the
other.
If a ll b and a  t, then
b  t.
t
a
b
Be Able to Name Special Pairs of Angles:
1. Alternate Interior Angles
2. Corresponding Angles
3. Alternate Exterior
4. Same-Side Interior Angles
2
1
3
4
6
5
7
8
Be Able to State the Relationship Between Any Two Angles:
1. Congruent Angles
2. Supplementary Angles
Exit Ticket

What three types of angles are congruent if
lines are parallel and cut by a transversal?

Homework – WB p. 60 (ALL)