Course: Applied Geometry Aim: Parallel Lines Aim: What are Transversals and Angle Pairs? Parallel...
-
Upload
millicent-rodgers -
Category
Documents
-
view
225 -
download
0
Transcript of Course: Applied Geometry Aim: Parallel Lines Aim: What are Transversals and Angle Pairs? Parallel...
Course: Applied GeometryAim: 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.
10x - 18
5x - 127x - 40
8x + 10
1. Intersecting lines form vertical angles that are opposite each other
and congruent. Therefore you can find
the value of x by putting 10x - 18 = 8x + 10 or 7x - 40 = 5x - 12
and solving for x.
Course: Applied GeometryAim: Parallel Lines
10x - 18
5x - 127x - 40
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
Do Now:
Course: Applied GeometryAim: Parallel Lines
A line that intersects more than one line is called a transversal.
l
pm is
a
transvers
al
m
Course: Applied GeometryAim: Parallel Lines
Exterior zone
Zones formed by
l
m
Interior zone
Exterior zone p
Course: Applied GeometryAim: Parallel Lines
Alternate Sides formed by
l
p
mExterior zone
Exterior zone
Interior zone
Course: Applied GeometryAim: Parallel Lines
The Importance of Parallel
Course: Applied GeometryAim: Parallel Lines
Two or more lines are parallel if and only if the lines lie in the same plane but do not intersect.
| | means “is parallel to”
p
DC
l
A B
AB | | CD or
l | | p
Course: Applied GeometryAim: Parallel Lines
Angles formed by
l
p
m
41
58
23
67
2 and 3 are congruent vertical angles
6 and 7 are congruent vertical angles
l | | p
If l | | p then 2 3 6 7
Course: Applied GeometryAim: Parallel Lines
Angles formed by
l
p
m
243
1
5 67 8
1 and 4 are congruent vertical angles
5 and 8 are congruent vertical angles
Since l | | p then 1 4 5 8
l | | p
Course: Applied GeometryAim: Parallel Lines
l
p
m
1
8
2
7
1 and 8 are alternate exterior angles
2 and 7 are alternate exterior angles
If l | | p then 1 8
If l | | p then 2 7
A
Alternate Exterior AnglesAlternate Exterior Angles
If two parallel lines are cut by a transversal, then the Alternate ExteriorAlternate Exterior AnglesAngles formed are
congruent.
43
5 6
Course: Applied GeometryAim: Parallel Lines
l
p
m
21
7 8
4
5
3
6
3 and 6 are alternate interior angles
4 and 5 are alternate interior angles
If l | | p then 3 6
If l | | p then 4 5
A
Alternate InteriorAlternate Interior AnglesAngles
If two parallel lines are cut by a transversal, then the Alternate InteriorAlternate Interior AnglesAngles formed are
congruent.
Course: Applied GeometryAim: Parallel Lines
l
p
m
21
7 8
3
5
4
6
3 and 5 are interior angles
3 and 6 are interior angles
If l | | p then 3 & 5 are supplementary
If l | | p then 3 & 5 are supplementary
InteriorInterior Angles on Same SideAngles on Same Side
If two parallel lines are cut by a transversal, then the InteriorInterior Angles Angles on the same side of the
transversal are supplementary.
Course: Applied GeometryAim: Parallel Lines
l
p
m
243
1
5 67 8
Corresponding Angles
A
Corresponding AnglesCorresponding Angles
If two parallel lines are cut by a transversal, then the Corresponding AnglesCorresponding Angles formed are congruent.
3 and 72 and 61 and 5
4 and 63 72 61 5
4 6
If l | | p then
Course: Applied GeometryAim: Parallel Lines
l
p
m
l is parallel to m
w xyz
qprs
Name the exterior anglesName the interior anglesName the corresponding anglesName the alternate interior anglesName the alternate exterior angles
Course: Applied GeometryAim: Parallel Lines
l
p
mFind the measure of each angle if 1 = 1370.
13 4
5 67 8
430
1370
1370
430
1370 430
1370
2
430
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.
Course: Applied GeometryAim: Parallel Lines
AB | | CD Find the measure of each angle if AHF = 8x - 20 and CGH = 4x + 44.
1080
E
GC D
H B
F
AHF and CGH are Corresponding Angles and therefore are congruent
8x - 20 = 4x + 44
4x - 20 = 44
4x = 64
x = 16
8(16) - 20 = 1080
1080
1080
1080
A
1800 - 1080 = 720
720
720
720
720
Course: Applied GeometryAim: Parallel Lines
The measure of b is twice the measure of a. What is the measure of each angle.
C D
B
F
A
b
a
AB | | CD
Course: Applied GeometryAim: Parallel Lines
The measure of a is five times the measure of b. What is the measure of y.
C D
B
F
A
ba
AB | | CDy
Course: Applied GeometryAim: Parallel Lines
Give two ways to find the measure of y.
C D
B
F
A zx
AB | | CD150o
y
Course: Applied GeometryAim: Parallel Lines
Find the measure of all angles.
C
D
B
G
Aqp
AB | | CD | | EF75o
E
F
o
sr
vu
xw
zy
Course: Applied GeometryAim: Parallel Lines
Skew Lines
Lines in space that never meet and are not in the same plane are skew lines.
A
B C
DE
F