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Complimentary Angles,
Supplementary Angles, and
Parallel Lines
Adjacent angles are “side by side”
and share a common ray.
45º
15º
These are examples of adjacent
angles.
80º
35º
45º
55º
85º
130º
20º
50º
These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º
When 2 lines intersect, they make
vertical angles.
75º
105º
105º
75º
Vertical angles are opposite one
another.
75º
105º
105º
75º
Vertical angles are congruent
(equal).
150º
30º
30º
150º
Supplementary angles add up to
180º.
40º
120º
60º
Adjacent and Supplementary Angles
140º
Supplementary Angles
but not Adjacent
Complementary angles add up to
90º.
30º
40º
60º
Adjacent and Complementary Angles
50º
Complementary Angles
but not Adjacent
Parallel Lines and Planes
You will learn to describe relationships among lines,
parts of lines, and planes.
In geometry, two lines in a plane that are always the same
parallel lines
distance apart are ____________.
No two parallel lines intersect, no matter how far you extend them.
Parallel Lines and Planes
Definition of
Parallel
Lines
Two lines are parallel if they are in the same plane and
intersect
do not ________.
Parallel Lines and Transversals
In geometry, a line, line segment, or ray that intersects two or more lines at
transversal
different points is called a __________
A
2
1
4
5
8
6
7
3
l
m
B
AB
is an example of a transversal. It intercepts lines l and m.
Note all of the different angles formed at the points of intersection.
Parallel Lines and Transversals
Definition of
Transversal
In a plane, a line is a transversal if it intersects two or more
lines, each at a different point.
The lines cut by a transversal may or may not be parallel.
Parallel Lines
Nonparallel Lines
l
1 2
4 3
lm
t
1 2
4 3
m
5 6
8 7
c
5 6
8 7
b || c
t
is a transversal for l and m.
b
r
r
is a transversal for b and c.
Parallel Lines and Transversals
Two lines divide the plane into three regions.
The region between the lines is referred to as the interior.
The two regions not between the lines is referred to as the exterior.
Exterior
Interior
Exterior
Parallel Lines and Transversals
eight angles are formed.
When a transversal intersects two lines, _____
These angles are given special names.
l
1 2
4 3
m
5 6
8 7
t
Interior angles lie between the
two lines.
Exterior angles lie outside the
two lines.
Alternate Interior angles are on the
opposite sides of the transversal.
Alternate Exterior angles are
on the opposite sides of the
transversal.
Consecutive Interior angles are on
the same side of the transversal.
Parallel Lines and Transversals
Theorem 4-1 If two parallel lines are cut by a transversal, then each pair of
congruent
Alternate
alternate interior angles is _________.
Interior
Angles
1 2
4 3
5 6
8 7
4  6
3  5
Parallel Lines and Transversals
Theorem 4-2 If two parallel lines are cut by a transversal, then each pair of
supplementary
Consecutive consecutive interior angles is _____________.
Interior
Angles
1 2
4 3
5 6
8 7
4  5  180
3  6  180
Parallel Lines and Transversals
Theorem 4-3 If two parallel lines are cut by a transversal, then each pair of
congruent
Alternate
alternate exterior angles is _________.
Exterior
Angles
1 2
4 3
5 6
8 7
1  7
2  8
Transversals and Corresponding Angles
When a transversal crosses two lines, the intersection creates a number of
angles that are related to each other.
Note 1 and 5 below. Although one is an exterior angle and the other is an
interior angle, both lie on the same side of the transversal.
corresponding angles
Angle 1 and 5 are called __________________.
l
1 2
4 3
m
5 6
8 7
t
Give three other pairs of corresponding angles that are formed:
4 and 8
3 and 7
2 and 6
Transversals and Corresponding Angles
Postulate 4-1 If two parallel lines are cut by a transversal, then each pair of
congruent
Corresponding corresponding angles are _________.
Angles
Transversals and Corresponding Angles
Types of angle pairs formed when
a transversal cuts two parallel lines.
Concept
Summary
Congruent
Supplementary
alternate interior
consecutive interior
alternate exterior
corresponding
Transversals and Corresponding Angles
s
s || t and c || d.
Name all the angles that are
congruent to 1.
Give a reason for each answer.
1 2
5 6
9
10
13 14
3  1
corresponding angles
6  1
vertical angles
8  1
alternate exterior angles
9  1
corresponding angles
14  1
alternate exterior angles
11  9  1
corresponding angles
16  14  1
corresponding angles
t
3
7
11 12
15 16
c
4
8
d