Download Parallel Lines

Aim: What are Transversals and
Angle Pairs? Parallel Lines?
Do Now:
Below are 2 intersecting straight
lines. Describe 2 different methods
of finding the value of x.
1. Intersecting lines
form vertical angles that
10x - 18
are opposite each other
7x - 40
5x - 12
and congruent.
Therefore you can find
8x + 10
the value of x by putting
10x - 18 = 8x + 10 or
7x - 40 = 5x - 12 and
solving
for x.
Course: Applied Geometry
Aim: Parallel Lines
Do Now:
10x - 18
7x - 40
5x - 12
8x + 10
2. There are 4 linear pair
in this diagram: angles
that are adjacent and
supplementary.
Therefore you can find
the value of x by solving
any of four equations:
10x - 18 + 5x - 12 = 180
5x - 12 + 8x + 10 = 180
8x + 10 + 7x - 40 = 180
7x - 40 + 10x - 18 = 180
x = 14
Aim: Parallel Lines
Course: Applied Geometry
A line that intersects more than one line is
called a transversal.
m
l
p
Aim: Parallel Lines
Course: Applied Geometry
Zones formed by
m
Exterior zone
l
Interior zone
Exterior zone
Aim: Parallel Lines
p
Course: Applied Geometry
Alternate Sides formed by
m
Exterior zone
l
Interior zone
p
Exterior zone
Aim: Parallel Lines
Course: Applied Geometry
The Importance of Parallel
Aim: Parallel Lines
Course: Applied Geometry
Two or more lines are parallel if and
only if the lines lie in the same plane
but do not intersect.
A
B
l
AB | | CD
or
l || p
p
C
D
| | means “is parallel to”
Aim: Parallel Lines
Course: Applied Geometry
Angles formed by
l || p
m
1
3
5
7
2
l
4
6
8
p
2 and 3 are congruent vertical angles
6 and 7 are congruent vertical angles
Course: Applied Geometry
Aim: Parallel Lines
If l | | p then
2  3  6  7
Angles formed by
m
l || p
1
3
5
7
2
l
4
6
8
p
1 and 4 are congruent vertical angles
5 and 8 are congruent vertical angles
Since l | | p then
1  4  5  Course:
8 Applied Geometry
Aim: Parallel Lines
Alternate Exterior Angles
m
2
1
3
5
7
l
4
6
8
p
1 and 8 are alternate exterior angles
If l | | p then 1  8
2 and 7 are alternate exterior angles
If l | | p then 2  7
A
If two parallel lines are cut by a transversal, then
the Alternate Exterior Angles formed are
Course: Applied Geometry
Aim: Parallel Lines
congruent.
Alternate Interior Angles
m
1
3
l
4
6
5
7
2
8
p
3 and 6 are alternate interior angles
If l | | p then 3  6
4 and 5 are alternate interior angles
If l | | p then 4  5
A
If two parallel lines are cut by a transversal, then
the Alternate Interior Angles formed are
Course: Applied Geometry
Aim: Parallel Lines
congruent.
Interior Angles on Same Side
m
1
3
l
4
6
5
7
2
8
p
3 and 5 are interior angles
If l | | p then 3 & 5 are supplementary
3 and 6 are interior angles
If l | | p then 3 & 5 are supplementary
If two parallel lines are cut by a transversal, then
the Interior Angles on the same side of the
Course: Applied Geometry
Aim: Parallel Lines
transversal are supplementary.
Corresponding Angles
m
1
3
5
7
2
l
4
6
8
p
Corresponding Angles
1  5
1 and 5
2 and 6
2  6
If l | | p then
3  7
3 and 7
4 and 6
4  6
A parallel lines are cut by a transversal, then
If two
the Corresponding Angles formed are congruent.
Aim: Parallel Lines
Course: Applied Geometry
l is parallel to m
Name the alternate
exterior angles
interior
corresponding
angles
interior
exterior
angles
angles
angles
m
w
z
p
s
x
l
y
q
r
Aim: Parallel Lines
p
Course: Applied Geometry
Find the measure of each
angle if 1 = 1370.
m
0
1370
43
1
2
4
3
0
43
1370
0
1370
43
6
5
430 7 81370
l
p
Note: 1 and 2 are a linear pair. How
many other linear pairs are there in this
diagram?
7 other linear pairs - 2 & 4; 4 & 3;
3 & 1; 5 & 6; 6 & 8; 8 & 7;
and 7 & 5.
Aim: Parallel Lines
Course: Applied Geometry
AB | | CD Find the measure of
each angle if AHF = 8x - 20
and CGH = 4x + 44.
F
1080
A
720
720
H 1080
B
1080 720
720 G 1080
D
C
AHF and CGH are
E
Corresponding Angles and
therefore are congruent
8(16) - 20 = 1080
8x - 20 = 4x + 44
1800 - 1080 = 720
4x - 20 =
44
4x
=
64
Course: Applied Geometry
Aim: Parallel Lines
x
=
16
The measure of b is twice the measure of
a. What is the measure of each angle.
AB | | CD
A
a
B
b
C
F
Aim: Parallel Lines
D
Course: Applied Geometry
The measure of a is five times the measure
of b. What is the measure of y.
AB | | CD
y
A
B
a
b
C
F
Aim: Parallel Lines
D
Course: Applied Geometry
Give two ways to find the measure of y.
AB | | CD
A
150o
x
z
B
y
C
F
Aim: Parallel Lines
D
Course: Applied Geometry
Find the measure of all angles.
o
A
p
r
C
u
w
E
y
AB | | CD | | EF
75o
q
B
s
v
D
x
z
F
G
Aim: Parallel Lines
Course: Applied Geometry
Skew Lines
Lines in space that never meet and are
not in the same plane are skew lines.
E
D
B
C
A
F
Aim: Parallel Lines
Course: Applied Geometry