Download 1.4 Angles & their Measures

Warm-Up: Billiards (“Pool”)
• Who has played pool?
• What’s a “bank shot”?
• How do you know
where to hit the ball on
• the side?
• It’s all in the angles!
• Angles are the
foundation of geometry
1.4 Angles & their Measures
Objectives:
•Define: Angle, side, vertex, measure, degree,
congruent
•Name angles with the vertex always in the
middle
•Measure angles with a protractor
•Identify congruent angles
•Classify angles as acute, right, obtuse, or
straight
•Add and subtract angle measures using the
angle addition postulate
Angle symbol:
• 2 rays that share the same endpoint (or
initial point)
Sides – the rays XY & XZ
Y
5
Z
Named <YXZ, <ZXY (vertex is
always in the middle), or <X (if
it’s the only <X in the diagram).
X
Vertex – the common
endpoint; X
Angles can also be
named by a #. (<5)
In the figure, there are three different <Q’s (two
smaller ones and a larger one). therefore, none
of them should be called <B. The vertex is
ALWAYS in the middle of the name
Example 1: Naming Angles
One angle only:
< EFG or < GFE
Three angles:
< ABC or < CBA
< CBD or < DBC
< ABD or < DBA
Angle Measurement
Postulate 3: Protractor Post.
• The rays of an angle
can be matched up
with real #s (from 1 to
180) on a protractor
so that the measure
of the < equals the
absolute value of the
difference of the 2 #s.
55o
20o
m<A = 55-20
= 35o
Interior or Exterior?
• B is ___________
in the interior
• C is ___________
in the exterior
on the <
• D is ___________
B
C
D
A
Adjacent Angles
• 2 angles that share a common vertex & side,
but have no common interior parts.
(they have the same vertex, but don’t overlap)
such as <1 & <2
2
1
Postulate 4:Angle Addition Postulate
Example 2:
m < FJH = m < FJG + m < GJH
m < FJH = 35° + 60°
Example 3:
.
S
P
If m<QRP=5xo,
m<PRS=2xo, &
m<QRS=84o, find x.
5x+2x=84
Q
7x=84
x=12
m<QRP=60o m<PRS=24o
R
Types of Angles
• Acute angle – Measures between 0o & 90o
• Right angle –
Measures exactly 90o
• Obtuse angle – Measures between 90o & 180o
• Straight angle –Measures exactly 180o
Example 4: Classifying Angles
• A. straight
• B. acute
• C. obtuse
Example 5:
• Name an acute angle
<3, <2, <SBT, or <TBC
• Name an obtuse angle
<ABT
• Name a right angle
<1, <ABS, or <SBC
• Name a straight angle
<ABC
S
T
3
1
2
A
B
C
Assignment
General 1.4 A
Honors 1.4 B