8-2

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8-2 Measuring and Classifying Angles8-2 Measuring and Classifying Angles

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

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8-2 Measuring and Classifying Angles

Warm Up

1. Draw two points. Label one point A and

the other point B.

2. Draw a line through points A and B.

3. Draw a ray with A as an endpoint and C

as a point on the ray.

4. Name all the rays in your drawing.

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AB, BA, and AC

A B

C

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Problem of the Day

The measure of Jack’s angle is twice that of Amy’s and half that of Nate’s. The sum of the measures of all the angles is equal to 105°. What is the measure of each student’s angle?

Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°

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Learn to name, measure, draw, and classify angles.

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Vocabulary

anglevertexacute angleright angleobtuse anglestraight angle

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An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.

Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees.

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Additional Example 1: Measuring an Angle with a Protractor

Use a protractor to measure the angle.

• Place the center point of the protractor on the vertex of the angle.

G H

F

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Additional Example 1 Continued


• Place the protractor so that ray GH passes through the 0° mark.

G H

F

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• Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses.



G H

F

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mFGH is read “the measure of angle FGH.”

Reading Math

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• The measure of FGH is 120°. Write this as m FGH = 120°.



G H

F

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Check It Out: Example 1


H I

G

• Place the center point of the protractor on the vertex of the angle.

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Check It Out: Example 1 Continued


• Place the protractor so that ray HI passes through the 0° mark.

H I

G

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H I

G

• Using the scale that starts with 0° along ray HI, read the measure where ray HG crosses.

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H I

G

• The measure of GHI is 70°. Write this as m GHI = 70°.

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Additional Example 2: Drawing an Angle with a Protractor

Use a protractor to draw an angle that measures 80°.

• Draw a ray on a sheet of paper.

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• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.

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• Make a mark at 80° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 80°.

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• Draw a ray on a sheet of paper.

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• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.



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• Make a mark at 45° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 45°.



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An acute angle measures less than 90°.

A right angle measures exactly 90°.

Right angles are usually marked with a symbol.

Reading Math

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An obtuse angle measures more than 90° and less than 180°.

A straight angle measures exactly 180°.

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Additional Example 3: Classifying Angles

Classify each angle as acute, right, obtuse, or straight.

A. B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 90°, so it is a right angle.

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Classify each angle as acute, right, obtuse, or straight.

A. B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 180°, so it is a straight angle.

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Additional Example 4: Application

A welder used this piece of metal on his project. Classify X, Y, and Z.

X

W

Y

Z

X right

Y obtuse

Z acute

The angle is marked as a right angle.

The angle measures more than 90° and less than 180°.

The angle measures less than 90°.

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A metal jeweler used this piece of metal on her project. Classify A, B, and D.

D

C

A

B

A obtuse

B acute

D right The angle is marked as a right angle.

The angle measures more than 90° and less than 180°.

The angle measures less than 90°.

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Lesson Quiz

Use a protractor to draw an angle with the given measure. Tell what type of angle it is.

1. 140°

2. 20°

3. Draw a right angle.

4. Is the angle shown closer to 30° or 120°?

Check student drawings: acute

Check student drawings; obtuse

30°

8-2

Documents

Transcript of 8-2