Download Glossary Terms * Chapter 3

Chapter 3.2 Angles and Parallel Lines
Check.4.8 Apply properties and theorems about
angles associated with parallel and perpendicular
lines to solve problems.
Objective: To understand the relationship of angles
created by having a transveral crossing two
parallel lines.
Bellwork
• With a partner take one of the sheets from
the side table and follow the directions.
Angle Postulates and Theorems
Postulate/Theorem
Example
Corresponding Angles
Postulate
If two parallel lines are cut by a
transversal then each pair of
corresponding angles is congruent
1  5, 2  6, 3  8,
4  7
Alternate Interior
Angles Theorem
If two parallel lines are cut by a
transversal, then each pair of alternate
interior angles is congruent
4  5, 3  6
Consecutive Interior
Angles Theorem
If two parallel lines are cut by a
transversal, then each pair of
consecutive interior angles is
supplementary
m4 + m6 = 180
m3+ m5 = 180
Alternate Exterior
Angles Theorem
If two parallel lines are cut by a
transversal, then each pair of alternate
exterior angles is congruent
1  8, 2  7
Perpendicular
Transversal Theorem
In a plane, if a line is perpendicular to
one of two parallel lines, then it is
perpendicular to the other
1
3
5
8
7
6
2
4
Corresponding Angles Postulate
If two parallel lines are cut by a transversal then each pair of
corresponding angles is congruent
1  5
1
3
2  6
3  8
4  7
5
8
7
6
2
4
Determine Angle Measures
1
3
5
8
7
6
2
4
What does this Assume?
The lines are parallel
In the figure, m3 = 133
Find m6
• 3  8
• Corresponding Angles
• 8  6
• Vertical Angles
• 3  6
• Transitive Property
• m3 = m6
• Definition of congruent Angles
• 133 = m6
• Substitution
Determine Angle Measures
10
12 13
x
y
14 15
16 17
11
In the figure, x || y, m11 = 51
Find m16
• 51
Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is
perpendicular to the other
t
1
p
2
q
• p||q, t  p
• 1 is a right angle
• m1 = 90
• 1 2
Given : p||q, t  p
Prove : t  q
• m1=m2
• m2 = 90
• 2 is a right angle
• tq
• Given
• Def of  lines
• Definition of right
angle
• Corresponding
Angles Postulate
• Definition of
congruent angles
• Substitution
• Definition of Right
Angles
• Def of  lines
Find the measure of GHI
•
•
•
•
•
Draw an Auxiliary Line
EHK AEK, alternate interior angles
m EHK = 40
FHK  HFC, alternate interior angles
mFHK= 70
A
G
E
B
40
J
H
40
70
• GHI = 40 + 70=110
C
K
70
D
F
I
Find the measure of GHI
•
•
•
•
•
Draw an Auxiliary Line
EHK AEK, alternate interior angles
m EHK = 60
FHK  HFC, alternate interior angles
mFHK= 65
A
G
E
B
60
J
60
65
• GHI = 60 + 65 = 125
65
C
F
I
H
K
D
1
m1 = 3x +40, m2 = 2(y-10), and
m3 = 2x + 70
Find x and y
F
3
G
E
2
4
H
m1 = m3
By Corresponding Angles
3x +40 = 2x + 70
-2x-40 -2x -40
x = 30
m1 = m2
Alternate Exterior Angles
3x +40 = 2(y-10)
3(30) + 40 = 2y -20
130 = 2y -20
150 = 2y
75 = y
Practice Assignment
•
Block Page 181, 12 - 36 every 4th