Transcript Slide 1 - Lyndhurst School District

Parallel 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.
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 iff 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.
Consectutive 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 is _________.
Angles