Download Chapter 1.4 Angles.notebook

Chapter 1.4 Angles.notebook
January 09, 2013
1.4 Measuring Angles
Objective: To find the measures of angles
M.2.B.
Performance Standard 1.6, 3.4, 3.5 DOK­1, 2
Knowledge MA 3
Postulate 1.7­ Protactor Postulate (similar to ruler postulate)
We can measure angles in terms of real numbers from 0 to 180 degrees.
What is an angle???
Angle­ Formed by two rays with the same endpoint.
Vertex­ the endpoint of an angle Sides­ Each ray of the angle
How do you measure angles???
How do you NAME angles???
E
Name the following angles:
A
2
B
1
D
Practice with handout.
F
C
How do you CLASSIFY angles???
Acute angle­ An angle that measures between 0 and 90 degrees.
Right angle­ An angle that measures 90 degrees.
Obtuse angle­ An angle that measures between 90 and 180 degrees.
Straight angle­ An angle that measures 180 degrees.
Aug 26­12:48 PM
Jul 24­7:21 AM
Postulate 1­8: Angle Addition Postulate­ Adjacent angle measures can be added together to form a large angle measure.
C
A
m < ABC + m < CBD = m < ABD
D
B
EX 1) m <ZTF = 125
m <UTF = 50 Find m <ZTU
Z
U
T
Jul 30­12:55 PM
F
Jul 24­7:23 AM
B
A
m < AOB = 3x + 12
m < BOC = 8x + 34
m < AOD = 6x + 114
Find x.
EX 3)
EX 2)
E
C
D
F
m < CDE= x+4 m<EDF=x+20.
Find x=
m<CDE
m<EDF
C
D
O
Jul 24­7:54 AM
Jul 24­7:57 AM
1
Chapter 1.4 Angles.notebook
January 09, 2013
Congruent angles­ Angles that have the exact same measure.
Bisector­ Cuts an angle or a segment into two equal parts.
2.5 Proving angles congruent.
Vertical Angles ­ Complementary Angles­ Two angles whose measures have the sum of 90 degrees.
EX. 4) BX bisects <ABC. If m<ABX = 5x, m<XBC = 3x+10, find x and m<ABC. A
Supplementary Angles­ Two angles whose measures have the sum of 180 degrees.
X
B
C
Jul 24­8:20 AM
Jul 24­8:26 AM
Name the complement and supplement of each angle and the measure of the angle vertical to the given angle.
Supplement
Vertical
WARNING: NOT IN THE BOOK
WARNING: NOT IN THE BOOK
Complement 25
108
90
56
125
Aug 26­12:55 PM
Jul 24­7:21 AM
Jul 24­8:17 AM
2