Download Parallel Lines and Transversals

Parallel Lines
and Angles
Vertical Angles
• Vertical Angles are angles that are
opposite each other at an intersection.
• Vertical Angles are equal
1
2
3
4
Angles 1 and 4 are vertical angles
Angles 2 and 3 are vertical angles
On your notesheet: Write a word and a picture
definition for vertical angles.
Supplementary Angles
• Supplementary angles are angles that
form lines (also called linear pairs)
• Supplementary angles add up to 180
1
2
3
4
Angles 1 and 2 are supplementary, Angles 1 and 3 are supplementary
Angles 2 and 4 are supplementary, Angles 3 and 4 are supplementary
On your notesheet: Write a word and a picture definition
for supplementary angles.
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 ________.
- This means the lines never touch
- This means the lines have the same slope
- This means the lines are always the same distance apart
-
The symbol for parallel is two vertical lines (II). For example
if line m and line t are parallel you could write m II t.
On your notesheet: Write a verbal and picture definition of parallel lines
On your paper: #1. What are three ways to describe how lines are parallel?
#2. What is the symbol for parallel?
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 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.
Alternate Interior angles are between
the two lines on the opposite sides of
the transversal. Ex. 4 and 6, 3 and 5
Consectutive Interior angles between
the two lines are on the same side of
the transversal. Ex. 4 and 5, 3 and 6
Alternate Exterior angles are outside the
two lines on the opposite sides of the
transversal. Ex. 1 and 7, 2 and 8
Corresponding angles are in the same position
at each intersection. Ex. 1 and 5, 2 and 6,
4 and 8, 3 and 7
l
1 2
4 3
m
5 6
8 7
t
Parallel Lines and Transversals
Alternate
If two parallel lines are cut by a transversal, then
Interior
each pair of
Angles
congruent (equal)
Alternate interior angles is _________.
between the
two lines on
the opposite
1 2
sides of the
4 3
transversal.
5 6
Ex. 4 and 6,
8 7
3 and 5
Angles 4 and 6 are alternate interior angles so we
know 4  6
On your paper: #3. Write down one other pair of alternate interior angles.
Parallel Lines and Transversals
Consecutive If two parallel lines are cut by a transversal, then
Interior
each pair of consecutive interior angles is
supplementary (add to 180)
Angles
_____________.
between the
two lines are
on the same
1 2
side of the
4 3
transversal.
5 6
Ex. 4 and 5,
8 7
3 and 6
Angles 4 and 5 are consecutive interior angles so
we know: 4  5  180
On your paper: #4. Write down one other pair of consecutive interior angles.
Parallel Lines and Transversals
Alternate
If two parallel lines are cut by a transversal, then
Exterior
congruent
each pair of alternate exterior angles is _________.
Angles
outside the
two lines on
the opposite
1 2
sides of the
4 3
transversal.
5 6
Ex. 1 and 7,
8 7
2 and 8
Angle 1 and 7 are alternate exterior angles so we
know: 1  7
On your paper: #5. Write down one other pair of alternate exterior angles.
Parallel Lines and Transversals
Corresponding If two parallel lines are cut by a transversal, then
Angles
each pair of corresponding angles is _________.
congruent
are in the
same position
at each
l
1 2
intersection.
4 3
Ex. 1 and 5,
m
2 and 6,
5 6
8 7
4 and 8,
3 and 7
t
Angle 1 and 5 are both in the upper left of each
intersection so they are corresponding angles and
we then know angle 1=angle 5
On your paper: #6. Write down three other pairs of corresponding angles.
Transversals and Corresponding Angles
Concept
Summary
Types of angle pairs formed when
a transversal cuts two parallel lines.
Congruent
Supplementary
alternate interior
consecutive interior
alternate exterior
corresponding
On your notesheet: Under “Special pair of Angles” for each pair
write equal or supplementary, then using the examples on the
notesheet write one pair from A and B.
Turn in your half piece of paper. Go to a table and complete your notesheet
page on parallel lines. After you have completed this, start the next sheet in
your packet. Whatever you don’t complete is homework for tonight.