Transcript Slide 1

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.
C
AB, BA, and AC
A
B
8-2 Measuring and Classifying Angles
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°
8-2 Measuring and Classifying Angles
Learn to name, measure, draw, and
classify angles.
8-2 Measuring and Classifying Angles
Vocabulary
angle
vertex
acute angle
right angle
obtuse angle
straight angle
8-2 Measuring and Classifying Angles
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 must be the
vertex.
Angles are measured in degrees. The
number of degrees determines the type
of angle. Use the symbol ° to show
degrees.
8-2 Measuring and Classifying Angles
Additional Example 1: Measuring an Angle with a
Protractor
Use a protractor to measure the angle. Tell what
angle it is.
F
H
G
• Place the center point of the protractor on
the vertex of the angle.
8-2 Measuring and Classifying Angles
Additional Example 1 Continued
Use a protractor to measure the angle.
F
H
G
• Place the protractor so that ray GH passes
through the 0° mark.
8-2 Measuring and Classifying Angles
Additional Example 1 Continued
Use a protractor to measure the angle.
F
H
G
• Using the scale that starts with 0° along ray
GH, read the measure where ray GF crosses.
8-2 Measuring and Classifying Angles
Reading Math
mFGH is read “the measure of
angle FGH.”
8-2 Measuring and Classifying Angles
Additional Example 1 Continued
Use a protractor to measure the angle.
F
H
G
• The measure of FGH is 120°. Write this
as m FGH = 120°.
8-2 Measuring and Classifying Angles
Check It Out: Example 1
Use a protractor to measure the angle.
G
H
I
• Place the center point of the protractor on
the vertex of the angle.
8-2 Measuring and Classifying Angles
Check It Out: Example 1 Continued
Use a protractor to measure the angle.
G
H
I
• Place the protractor so that ray HI passes
through the 0° mark.
8-2 Measuring and Classifying Angles
Check It Out: Example 1 Continued
Use a protractor to measure the angle.
G
H
I
• Using the scale that starts with 0° along ray
HI, read the measure where ray HG crosses.
8-2 Measuring and Classifying Angles
Check It Out: Example 1 Continued
Use a protractor to measure the angle.
G
H
• The measure of
m GHI = 70°.
I
GHI is 70°. Write this as
8-2 Measuring and Classifying Angles
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.
8-2 Measuring and Classifying Angles
Additional Example 2 Continued
Use a protractor to draw an angle that measures 80°.
• 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.
8-2 Measuring and Classifying Angles
Additional Example 2 Continued
Use a protractor to draw an angle that measures 80°.
• 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°.
8-2 Measuring and Classifying Angles
Check It Out: Example 2
Use a protractor to draw an angle that measures 45°.
• Draw a ray on a sheet of paper.
8-2 Measuring and Classifying Angles
Check It Out: Example 2 Continued
Use a protractor to draw an angle that measures 45°.
• 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.
8-2 Measuring and Classifying Angles
Check It Out: Example 2 Continued
Use a protractor to draw an angle that measures 45°.
• 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°.
8-2 Measuring and Classifying Angles
An acute angle measures
greater than 0° and less than
90°.
A right angle measures
exactly 90°.
Reading Math
Right angles are usually marked with a
symbol.
8-2 Measuring and Classifying Angles
An obtuse angle
measures greater
than 90° and less
than 180°.
A straight angle
measures exactly
180°.
8-2 Measuring and Classifying Angles
Additional Example 3: Classifying Angles
Classify each angle as acute, right, obtuse, or straight.
A.
The angle measures
less than 90°, so it is an
acute angle.
B.
The angle measures
exactly 90°, so it is a
right angle.
8-2 Measuring and Classifying Angles
Check It Out: Example 3
Classify each angle as acute, right, obtuse, or straight.
A.
The angle measures
less than 90°, so it is an
acute angle.
B.
The angle measures
exactly 180°, so it is a
straight angle.
8-2 Measuring and Classifying Angles
Additional Example 4: Application
A welder used this piece of metal on his project.
Classify X, Y, and Z.
Y
X
Z
W
X right
The angle is marked as a right angle.
Y obtuse
The angle measures greater than 90°
and less than 180°.
Z acute
The angle measures less than 90°.
8-2 Measuring and Classifying Angles
Check It Out: Example 4
A metal jeweler used this piece of metal on her
project. Classify A, B, and D.
A
D
B
C
B acute
The angle measures greater than 90°
and less than 180°.
The angle measures less than 90°.
D
The angle is marked as a right angle.
A obtuse
right
8-2 Measuring and Classifying Angles
Lesson Quiz
Use a protractor to draw an angle with the
given measure. Tell what type of angle it is.
1. 140° Check student drawings; obtuse
2. 20°
Check student drawings; acute
3. Draw a right angle.
4. Is the angle shown closer to 30° or 120°?
30°