Transcript Parallels and Transversals

Do Now
A
B
C
D
1. Name a line that does not intersect with
line AC.
2. What is the intersection of lines AB and
DB?
3.1 Identify Pairs of Lines and
Angles
3.2 Use Parallel Lines and
Transversals
Objective: To identify angle pairs
formed by three intersecting lines; to
use angles formed by parallel lines and
transversals
Parallel Lines
Lines that
do not
Intersect
and are
coplanar
Parallel Planes
Planes that
Do not
Intersect
Skew Lines
Lines that do
Not intersect
and are not
Coplanar.
Transversal
• Transversal: a line that intersects two or
more coplanar lines.
Angles formed by a transversal
• There are 4 types of angles formed by a
transversal.
Corresponding angles
1
5
Angles 1 and 5 are corresponding
Because they have corresponding
Positions.
Corresponding angles of Parallel
Lines
1
k
m
5
The corresponding angles 1 and 5
Are congruent to each other
Because lines k and m are parallel
To each other.
Alternate Exterior Angles
1
8
Angles 1 and 8 are alternate
Exterior angles because they are
On alternate sides of the
Transversal and are exterior
Of the two lines.
Alternate Exterior angles of
Parallel Lines
k
m
1
8
The alternate exterior angles
1 and 8 are congruent to each
other because lines k and m are
Parallel to each other.
Alternate Interior Angles
3
6
Angles 3 and 6 are alternate
interior angles because they are
On alternate sides of the
Transversal and on the interior
Of the two lines.
Alternate Interior angles of
Parallel Lines
k
m
3
6
The alternate interior angles
3 and 6 are congruent to each
other because lines k and m are
Parallel to each other.
Consecutive Interior Angles
4
6
Angles 4 and 6 are consecutive
Interior angles because they are
On the same side of the transversal
And are inside the two lines.
Consecutive Interior angles of
Parallel Lines
k
m
4
6
The consecutive interior angles
4 and 6 are supplementary to
each other because lines k and m
are parallel to each other.
Parallel lines cut by a
transversal.
• When two parallel lines are cut by a
transversal the following relationships are
true.
– Corresponding angles are congruent
– Alternate exterior angles are congruent
– Alternate interior angles are congruent
– Consecutive interior angles are
supplementary.
Example 1:
1
2
3 4
5 6
7
8
Name all pairs of corrsponding,
alternate interior, alternate
exterior, and consecutive
interior angles.
Example: Classify the angle pair
x
y
Example: Classify the angle pair
m
n
Example: Classify the angle pair
p
q
Example 2: Solve for the variable
2p
120
Example 3: Solve for the variable
x
80
Example 4: Find all the missing
angle measures
105