Download Section 1.4 Angles and Their Measures

Section 1.4
Angles and Their Measures
5/9/2017
Goals
• Use angle postulates
• Classifying Angles
Vocabulary
• ANGLE
CONSISTS OF TWO DIFFERENT RAYS
THAT HAVE THE SAME INITIAL POINT.
A
<ABC
<CBA
B
C
Sides
• The rays that make up the angle
A
B
C
Vertex
• The initial point is the vertex of the angle
Vertex
Congruent Angles
• Angles with the same measure.
Interior
• A point is in the interior of an angle if it is
between points that lie on each side of the
triangle
Interior
Exterior
• A point is in the exterior of an angle if it is
not on the angle or in its interior.
Exterior
Acute Angle
0  mA  90


A
Right Angle
mA  90

A
Obtuse Angle
90  mA  180

A

Straight Angle
mA  180

A
Adjacent Angles
• Two angles that share a common vertex
and side, but have no common interior
points.
P
R
S
T
RSP and PST are adjacent, PS is
the common side and S is the
common vertex
Postulates
Protractor Postulate
Angle Addition Postulate
• If P is in the interior of RST, then
m RSP + m PST = m RST
m RSP
m PST
Example 1
• Name the angles in the figure.
M

 P
N

O

Example 2
• The backyard of a house is illuminated by a
light fixture that has two bulbs. Each bulb
illuminates an angle of 120º. If the angle
illuminated only by the right bulb is 35º,
what is the angle illuminated by both
bulbs?
Example 3
• Plot the points A(-3, -1), B(-1, 1), C(2, 4),
D(2, 1), and E(2, -2). Then measure and
classify the following angles as acute,
right, obtuse, or straight.
• DBE
• EBC
• ABC
• ABD
Example 4
• Use a protractor to draw two adjacent
angles LMN and NMO so that LMN is
acute and LMO is straight.
Homework
1.4
#2 – 22 even, 23–25all, 26 – 48 even