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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Sect. 1.4 ­ Angle Measure
Ray ­ is a part of a line so that there is one
one endpoint and it extends in the other direction indefinitely.
R
S
Ray RS or RS
A point on a line determines exactly two
rays which are called opposite rays and
opposite rays are collinear.
A B C
BA and BC are opposite rays
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Angle ­ Formed when two non­collinear rays
have a common endpoint. The rays
are the sides of the angle and the
common endpoint is the vertex.
P
O
Side OP, side OQ
vertex O
1
Q
An angle is named by using 3 letters (points)
where the middle letter is the vertex. Or,
by a single letter (the vertex) If there is
only one angle at that vertex. Or, the angle can be numbered and named as POQ, QOP, O, or
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
An angle divides the plane into three parts.
Points that lie on the angle.
Points in the interior of the angle.
Points in the exterior of the angle.
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Ex.: Use the figure to answer the questions.
1. Name all angles that
have B as a vertex.
2. Name the sides of 5.
3. Write another name
for 6.
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Angles ­ are measured in units called degrees.
When the distance around the circle is divided into 360 equal parts, each one is
called a degree.
Angles are classified by their measures as
Acute, Right, and Obtuse (also straight)
m A< 90
m B=90
Mr. VanKeuren / G.H.S / Geometry / 2014
90< m C <180
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Protractors are used to measure angles
Ex.: Classify each angle and find
their measure.
a. MOQ
80
Q
90
100
110
70
60
P
110
50
100
90
130
140
50
130
140
30
70
60
120
40
120
80
0°
40
150
30
150
160
20
b. MOP
20
160
10
0
10
170
0
180
O
170
180
M
c. POQ
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Angles that have equal measures are called congruent angles and can be marked
out on figures using matching arcs (much the same way as congruent segments are marked out). Since m TUV = m XYZ, then
TUV XYZ.
Mr. VanKeuren / G.H.S / Geometry / 2014
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Sect. 1.4
G.CO.1 / G.CO.12 / Math Pract. 5,6
Angle Bisector ­ a ray that divides an angle
into two congruent angles.
A
D
B
C
BD is the angle bisector of ABC
Mr. VanKeuren / G.H.S / Geometry / 2014
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