1. Parallel Lines and Planes
What You'll Learn
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 distance apart are ____________.
parallel lines
No two parallel lines intersect, no matter how far you extend them.

2. Parallel Lines and Planes
Definition of
Parallel
Lines
Two lines are parallel iff they are in the same plane and do not ________.
intersect

3. Parallel Lines and Transversals
What You'll Learn
You will learn to identify the relationships among pairs of interior and exterior angles formed by two parallel lines and a transversal.

4. Parallel Lines and Transversals
In geometry, a line, line segment, or ray that intersects two or more lines at
different points is called a __________
transversal B A l m 1 2 4 3 5 6 8 7
is an example of a transversal. It intersects lines l and m.
Note all of the different angles formed at the points of intersection.

5. 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. l m 1 2 3 4 5 7 6 8
Parallel Lines
t is a transversal for l and m. t 1 2 3 4 5 7 6 8 b c
Nonparallel Lines
r is a transversal for b and c. r

6. 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

7. Parallel Lines and Transversals
When a transversal intersects two lines, _____ angles are formed.
eight
These angles are given special names. l m 1 2 3 4 5 7 6 8 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. ?

8. Transversals and Corresponding Angles
What You'll Learn
You will learn to identify the relationships among pairs of
corresponding angles formed by two parallel lines and a
transversal.

9. 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.
Angle 1 and 5 are called __________________.
corresponding angles l m 1 2 3 4 5 7 6 8 t
Give three other pairs of corresponding angles that are formed:
4 and 8
3 and 7
2 and 6