Lesson 1.2 – Poolroom Math

Homework: 1.2/ 2-40 evens

Geometry HonorsHomework: 1.2/ 2-40 evens, 41-45, 48

ProtractorA 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?

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.

No!! The angles must be lined up properly.

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?

This angle measures 35°.

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°.

A revolution is an angle that equals exactly 360º.

Full Revolution

Reflex Angle

A reflex angle is greater than 180º and less than 360º.

It represents the largest amount of rotation.

Now, we will use a protractor to measure the reflex angle PQR.

Measuring Reflex Angles

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

<ADB + <ADC = 180°

<ADB and <ADC are adjacent angles

Adjacent Angles

Complementary AnglesTwo 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°

These two angles can be "pasted" together to form a right angle!

Complementary Angles

Adjacent Complementary Angles.

Supplementary AnglesTwo 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 °

Two angles that share a vertex and a side

to form a line.

Linear Pair of AnglesSpecial Supplementary Angles

Vertical AnglesOpposite 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 PointAngles around a point will always add up to 360°

The angles above all add to 360° 53° + 80° + 140° + 87° = 360°

We can find an unknown angle using this sum.

m< C = 360° − 298°

m < C = 62°

Example: What is angle “C"?

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°

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

20

C

J

D

E F

G

H

70

9070

20

90 Box in the corner indicates a right angle.

Find the measure of all the angles with vertex C

Final DrawingFind the measure of all the angles with vertex G.

52

B

A

F E

D

C

60

G

68

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