8.1 angles 1
Transcript of 8.1 angles 1
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Daily Homework Quiz For use after Lesson 7.3
Use a percent proportion to answer the question.
1. 28 is what percent of 80? 2. 15 is 5% of what number?
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Daily Homework Quiz For use after Lesson 7.3
Use a percent proportion to answer the question.
ANSWER 35%
1. 28 is what percent of 80? 2. 15 is 5% of what number?
ANSWER 300
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Chapter 8.1
Lines and Angles
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Essential Questions
• Why is it important to be able to identify congruent triangles in everyday life?
• Where in real life can you use the properties of isosceles and equilateral triangles?
• How are the relationships between lines and planes used in the real world?
• What areas in the real world are properties of parallel lines important?
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Chapter 8 Section 1
• Vocabulary 1-14
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Prerequisite Skills VOCABULARY CHECK
APoint: a figure without dimensions.
Line: a figure that extends without end in two opposite directions.
X Y XY
Ray: a figure that has one endpoint and extends without end in one direction.
C D CD
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• Plane : A flat surface that extends without end.
• Angle: a figure formed by two rays that begin at a common point called the vertex.
C
A
B
Vertex
Vertex: end point of the rays that form an angle.
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• Degree: unit of measure. 950
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Prerequisite Skills VOCABULARY CHECK
Identify the object with the review word from the list: point, line, ray, plane, angle, vertex, degree.
2.
1.
3.
ANSWER line
ANSWER point
ANSWER ray
4. A unit for measuring angles is a(n) ? .
ANSWER degree
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Classifying Angles
• Angles are classified by degrees.
• Acute - greater than 0 degrees but less than 90 degrees.
C
A
BThis is read “Angle ABC or Angle CBA, or just Angle B
ABC
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Classifying Angles
• Obtuse – angles measuring more than 90 degrees but less than 180 degrees.
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Classifying Angles
• Right Angles measure exactly 90 degrees and labeled with “square” in the corner of the angle.
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Classifying Angles• A straight angle “looks like” a straight line,
but it actually is an angle. It measures exactly 180 degrees.
A B C
180ABC m
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Two angles are complementary if the sum of their measures is 90 degrees.
70 °
20 °
70 + 20 = 90 degrees.
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• Are these complementary angles?
60 °
30 °
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• Two angles are supplementary if the sum of their measures is 180 degrees.
1 2 180m m
1 2
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GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary, supplementary, or neither.
1. m 1 = 79
m 2 = 101
SOLUTION
m 1+ m 2
= 79° + 101°
ANSWER
Hence, the angles are supplementary.
= 180
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GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary, supplementary, or neither.
2. m 1 = 64
m 1 = 36
SOLUTION
m 1+ m 2
= 100°
= 64 + 36
ANSWER
Hence, 1 and 2 are neither complementary nor supplementary.
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GUIDED PRACTICE for Example 1
Tell whether 1 and 2 are complementary, supplementary, or neither.
3. m 1 = 52
m 1 = 38
SOLUTION
m 1+ m 2
= 52 + 38
= 90
ANSWER
Hence, 1 and 2 are complementary.
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Vertical AnglesWhen two lines intersect at a point, they form
two pairs of vertical angles. They do not share a side, and they have the same measure.
1
3 42
Angles 1 & 2 are vertical angles and 3&4 are vertical angles.
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GUIDED PRACTICE for Example 2
Find the measures of the numbered angles.
SOLUTION
It is given that m 5 = 137 .
STEP 1
5 and 7 are vertical angles.Their measures are equal, so m 7 = 137 ° .
137°
43°
43°
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GUIDED PRACTICE for Example 2
Find the measures of the numbered angles.
SOLUTION
It is given that m 8 = 54 .
STEP 1
8 and 10 are vertical angles. Their measures are equal, so m 10 = 54 ° .
54°
126°
126°
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Homework
• Page 406 #1-11