Download Lesson 2.6 notes.notebook

Lesson 2.6 notes.notebook
September 19, 2011
Lesson 2.6: Definitions and Postulates Involving Angles
Angle Review
Definition: two rays with a common endpoint
INTERIOR
Ray/Side
Angle
Ray/Side
Vertex
EXTERIOR
Opposite Rays
when two rays make a straight line with 180 degrees
Protractor Postulate
Let O be a point on AB such that O is between A and B. Consider OA, OB, and all rays that can be drawn from O on one side of AB. These rays can be paired with the real numbers from 0 to 180 so that
1. OA is paired with 0 and OB is paired with 180.
2. If OP is paired with x and OQ is paired with y, then the number paired with POQ is |x ­ y|. This number is called the measure or degree measure, of POQ
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Lesson 2.6 notes.notebook
September 19, 2011
How can we find m MNO?
80
90
70
M
110
50
100
110
60
100
90
120
80
70
130
120
40
60
130
140
30
140
50
0°
40
150
150
O
30
20
160
160
10
20
170
0
170
10
180
180
0
N
R
Q
Find the m BEC.
B
80
90
110
60
110
50
100
90
80
70
130
140
50
130
140
30
120
60
120
40
C
100
70
0°
40
150
30
150
160
20
20
160
10
0
R
10
170
0
180
E
170
180
Q
2
Lesson 2.6 notes.notebook
September 19, 2011
Types of Angles
Acute
greater than 0 and less than 90
Right
equal to 90
Obtuse
greater than 90 and less than 180
Straight
equal to 180
Complementary Angles
two angles that add up to 90 degrees
38
25
each angle is the complement of the other
65
Supplementary Angles
52
two angles that add up to 180 degrees
each angle is the supplement of the other
23
157
61
119
3
Lesson 2.6 notes.notebook
September 19, 2011
Adjacent Angles
two angles in the same plane that share a common side and a common vertex
Linear Pair
two adjacent angles that are supplementary
What is the difference between supplementary angles and a linear pair?
Angle Addition Postulate
If point B is in the interior of angle AOC, then
m AOB + m BOC = m AOC
A
B
C
O
4
Lesson 2.6 notes.notebook
September 19, 2011
Find m PRQ.
Q
n + 2
2n ­ 17
P
R
T
Find m JMK and m KML.
J
K
2r + 6
60 ­ r
M
L
5
Lesson 2.6 notes.notebook
September 19, 2011
Congruent Angles
angles that are equal in measure
Angle Bisector
a line, segment, or ray that divides an angle in half
Homework
p. 96­97
#21­39 All
#43­48 All
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