1. Parallel Lines and TransversalsParallel Lines and Transversals
You will learn to identify the relationships among pairs of
interior and exterior angles formed by two parallel lines
and a transversal.
2. Parallel Lines and TransversalsParallel Lines and Transversals
In geometry, a line, line segment, or ray that intersects two or more lines at
different points is called a __________transversal
l
m
B
A
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.
1 2
34
5
7
6
8
3. Parallel Lines and TransversalsParallel Lines and Transversals
Definition of
Transversal
In a plane, a line is a transversal iff it intersects two or more
Lines, each at a different point.
The lines cut by a transversal may or may not be parallel.
l
m
1 2
34
5
7
6
8
ml
Parallel Lines
t is a transversal for l and m.
t
1 2
34
5
7
6
8
b
c
cb ||
Nonparallel Lines
r is a transversal for b and c.
r
4. Parallel Lines and TransversalsParallel 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
Exterior
Interior
5. l
m
1 2
34
5
7
6
8
Parallel Lines and TransversalsParallel Lines and Transversals
When a transversal intersects two lines, _____ angles are formed.eight
These angles are given special names.
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.
Consectutive Interior angles are on
the same side of the transversal.
Alternate Exterior angles are
on the opposite sides of the
transversal.
6. Parallel Lines and TransversalsParallel Lines and Transversals
Theorem 4-1
Alternate
Interior
Angles
If two parallel lines are cut by a transversal, then each pair of
Alternate interior angles is _________.
1 2
34
5
7
6
8
64 ∠≅∠ 53 ∠≅∠
congruent
7. Parallel Lines and TransversalsParallel Lines and Transversals
1 2
34
5
7
6
8
Theorem 4-2
Consecutive
Interior
Angles
If two parallel lines are cut by a transversal, then each pair of
consecutive interior angles is _____________.supplementary
18054 =∠+∠ 18063 =∠+∠
8. Parallel Lines and TransversalsParallel Lines and Transversals
1 2
34
5
7
6
8
Theorem 4-3
Alternate
Exterior
Angles
If two parallel lines are cut by a transversal, then each pair of
alternate exterior angles is _________.congruent
71 ∠≅∠ 82 ∠≅∠
9. Transversals and Corresponding AnglesTransversals and Corresponding Angles
You will learn to identify the relationships among pairs of
corresponding angles formed by two parallel lines and a
transversal.
10. Transversals and Corresponding AnglesTransversals and Corresponding Angles
l
m
1 2
34
5
7
6
8
t
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.
Angle 1 and 5 are called __________________.corresponding angles
Give three other pairs of corresponding angles that are formed:
4 and 8 3 and 7 2 and 6
11. Transversals and Corresponding AnglesTransversals and Corresponding Angles
Postulate 4-1
Corresponding
Angles
If two parallel lines are cut by a transversal, then each pair of
corresponding angles is _________.congruent
12. Transversals and Corresponding AnglesTransversals and Corresponding Angles
Concept
Summary
Congruent Supplementary
alternate interior
alternate exterior
corresponding
consecutive interior
Types of angle pairs formed when
a transversal cuts two parallel lines.
13. Transversals and Corresponding AnglesTransversals and Corresponding Angles
s t
c
d
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
s || t and c || d.
Name all the angles that are
congruent to 1.
Give a reason for each answer.
3 1 corresponding angles
6 1 vertical angles
8 1 alternate exterior angles
9 1 corresponding angles
11 9 1 corresponding angles
14 1 alternate exterior angles
16 14 1 corresponding angles
