ch 7 learning goal: plane geometry
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Ch 7 Learning Goal: PLANE GEOMETRY• Learn to describe the figures by using the terms of geometry (7-1)• Learn to name, measure, classify, estimate and draw angles (7-2)• Learn to understand relationship of angles (7-3)• Learn to classify the different types of lines (7-4)• Learn to classify triangles and solve problems involving angle and side
measures of triangles (7-5)• Learn to identify, classify, and compare quadrilaterals (7-6)• Learn to identify regular and not regular polygons and to find the angle
measures of regular polygons (7-7)• Learn to recognize, describe, and extend geometric patterns (7-8)• Learn to identify congruent figures and to use congruence to solve
problems (7-9)• Learn to use translations, reflections, and rotations to transform geometric
shapes (7-10)• Learn to identify line symmetry (7-11)• Learn to identify tessellations and shapes that can tessellate (7-12)
Page 324 #1-14 Answers
6th Grade Math HomeworkChapter 7-2
Page 328
#11-27ESTIMATING YOUR
ANSWERS!
7-2 Angles
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Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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
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 Amy’s and Trisha’s angles is equal to the sum of the measures of Jack’s and Nate’s angles. The sum of the measures of all the angles is equal to 180°. What is the measure of each student’s angle?
Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°; Trisha’s angle: 75°
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Today’s Learning Goal Assignment
Learn to name, measure, classify,
estimate, and draw angles.
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Vocabulary
anglevertexacute angleright angleobtuse anglestraight angle
Insert Lesson Title Here
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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: 90° means “90 degrees.”
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An acute angle measures less than 90°.
A right angle measures exactly 90°.
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An obtuse angle measures more than 90° and less than 180°.
A straight angle measures exactly 180°.
Math Internet Connect
go.hrw.com
Keyword: MR4 7-2
www.mathplayground.com
Measuring Angles with a Protractor!
http://www.mathplayground.com/measuringangles.html
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Additional Example 1: Measuring an Angle with a Protractor
Use a protractor to measure the angle. Tell what type of angle it is.
• Place the center point of the protractor on the vertex of the angle.
G H
F
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Additional Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
• 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.
Additional Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
G H
F
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• The measure of FGH is 120°. Write this as m FGH = 120°.
Additional Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
G H
F
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• Since 120° > 90° and 120° < 180°, the angle is obtuse.
Additional Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
G H
F
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Try This: Example 1
Use a protractor to measure the angle. Tell what type of angle it is.
H I
G
• Place the center point of the protractor on the vertex of the angle.
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Try This: Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
• Place the protractor so that ray HI passes through the 0° mark.
H I
G
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Try This: Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
H I
G
• Using the scale that starts with 0° along ray HI, read the measure where ray HI crosses.
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Try This: Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
H I
G
• The measure of GHI is 70°. Write this as m GHI = 70°.
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Try This: Example 1 Continued
Use a protractor to measure the angle. Tell what type of angle it is.
H I
G
• Since 70° < 90°, the angle is acute.
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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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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.
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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 make at 80°.
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Try This: Example 2
Use a protractor to draw an angle that measures 45°.
• 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.
Try This: Example 2 Continued
Use a protractor to draw an angle that measures 45°.
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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 make at 45°.
Try This: Example 2 Continued
Use a protractor to draw an angle that measures 45°.
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To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.
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Additional Example 3: Estimating Angle Measures
Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.
Think: The measure of the angle is about halfway between 90° and 180°. A good estimate would be 135°.
The angle measures 131°, so the estimate is reasonable.
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Try This: Example 3
Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.
Think: The measure of the angle is a little more than halfway between 0° and 90°. A good estimate would be 50°.
The angle measures 52°, so the estimate is reasonable.
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°?
acute
obtuse
Insert Lesson Title Here
30°
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