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Lesson 1.2 – Poolroom Math
Homework: 1.2/ 2-40 evens
Geometry Honors
Homework: 1.2/ 2-40 evens, 41-45, 48
Protractor
A device used to measure angles.
Measuring, calculating and drawing
angles...
Our learning objectives today
To use a protractor to:
a) measure acute and obtuse angles to the nearest
degree.
b) draw acute and obtuse angles to the nearest
degree.
To calculate angles on a straight line.
We use protractors to help us
measure angles
These are standard protractors.
When we use a protractor, we need to
line it up correctly with the angle.
You need to make sure the protractor is lined up
correctly.
Are these protractors ready to measure the
angle?
No!! The angles must be lined up properly.
Look for the upside down ‘T’ in
the middle of the straight line on
your protractor.
In this protractor look
for the hole in the
center.
These spots need to be exactly on the
vertex of your angle.
We also need to remember to
line up the base
One side of the angle must be lined up
with the base of the protractor.
It doesn’t matter which side.
What is the angle measure?
The side of the angle passes over 2 measurements:
145° and 35°. Which one is correct??
This is an acute angle. Therefore, the
measurement should be between 0 & 90°.
This angle measures 35°.
Full Revolution
A revolution is an angle that equals exactly 360º.
Reflex Angle
A reflex angle is greater than 180º and
less than 360º.
It represents the largest amount of rotation.
Measuring Reflex Angles
Now, we will use a protractor to measure the reflex
angle PQR.
To measure the reflex angle PQR,
1. Measure the smaller angle PQR.
2. Subtract from 360°.
Angle Bisector
The bisector of an angle,
also called the angle
bisector is the ray, line or
line segment that divides
the angle into two equal
parts (marked by slash marks).
.
D
Adjacent Angles
<ADB + <ADC = 180°
<ADB and <ADC are adjacent angles
Complementary Angles
Two angles are called complementary angles if the
sum of their degree measurements equals 90 degrees.
Example:
These two angles are complementary. Their sum is 90˚.
58° + 32° = 90°
Complementary Angles
These two angles can be "pasted" together to
form a right angle!
Adjacent Complementary Angles.
Supplementary Angles
Two angles are called supplementary angles if the sum
of their degree measurements equals 180 degrees.
Example:
These two angles are supplementary.
The sum of their measures is 180˚
139° +41° = 180 °
Linear Pair of Angles
Special Supplementary Angles
Two angles that share a vertex and a side
to form a line.
Vertical Angles
Opposite angles formed by intersecting lines .
For any two lines that meet, such as in the diagram below,
angle AEB and angle DEC are called vertical angles.
Angle BEC and angle AED are also vertical angles.
Vertical angles are congruent - have the same degree
measurement.
Angles Around a Point
Angles around a point will always add up to 360°
The angles above all add to 360°
53° + 80° + 140° + 87° = 360°
Example: What is angle “C"?
We can find an unknown angle using this sum.
To find the measure of angle C find the sum of the
known angles and subtract that from 360° .
Sum of known angles =
110° + 75° + 50° + 63° = 298°
m< C = 360° − 298°
m < C = 62°
Pool Room Math
Incoming angles = outgoing angles
Will the 4 ball land in the pocket??
Which path will the cue ball follow?
Will the blue ball land in a pocket?
More drawings
Find the measure of all the angles with vertex C
F
E
20
70
90
D
G
C
70
J
90
20
H
Box in the
corner
indicates a
right angle.
Final Drawing
Find the measure of all the angles with vertex G.
B
C
68
A
52
60
G
D
52
60
68
F
E