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8.1 angles 1

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  • 1. 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?
  • 2. 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? ANSWER 35% ANSWER 300
  • 3. Chapter 8.1 Lines and Angles
  • 4. 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?
  • 5. Chapter 8 Section 1
    • Vocabulary 1-14
  • 6. Prerequisite Skills VOCABULARY CHECK Point: a figure without dimensions. Line: a figure that extends without end in two opposite directions. X Y XY CD A Ray: a figure that has one endpoint and extends without end in one direction. C D
  • 7.
    • Plane : A flat surface that extends without end.
    • Angle: a figure formed by two rays that begin at a common point called the vertex.
    Vertex Vertex: end point of the rays that form an angle. C A B
  • 8.
    • Degree: unit of measure. 95 0
  • 9. 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
  • 10. Classifying Angles
    • Angles are classified by degrees.
    • Acute - greater than 0 degrees but less than 90 degrees.
    C A B This is read “Angle ABC or Angle CBA, or just Angle B
  • 11. Classifying Angles
    • Obtuse – angles measuring more than 90 degrees but less than 180 degrees.
  • 12. Classifying Angles
    • Right Angles measure exactly 90 degrees and labeled with “square” in the corner of the angle.
  • 13. Classifying Angles
    • A straight angle “looks like” a straight line, but it actually is an angle. It measures exactly 180 degrees.
    A B C
  • 14.
    • Two angles are complementary if the sum of their measures is 90 degrees.
    70 ° 20 ° 70 + 20 = 90 degrees.
  • 15.
    • Are these complementary angles?
    60 ° 30 °
  • 16.
    • Two angles are supplementary if the sum of their measures is 180 degrees.
    • 2
  • 17. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 1. m 1 = 79 m 2 = 101 m 1+ m 2 = 79 ° + 101 ° ANSWER Hence, the angles are supplementary. = 180
  • 18. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 2. m 1 = 64 m 1 = 36 m 1+ m 2 = 100 ° = 64 + 36 ANSWER Hence, 1 and 2 are neither complementary nor supplementary.
  • 19. GUIDED PRACTICE for Example 1 SOLUTION Tell whether 1 and 2 are complementary , supplementary , or neither . 3. m 1 = 52 m 1 = 38 m 1+ m 2 = 52 + 38 = 90 ANSWER Hence, 1 and 2 are complementary.
  • 20. Vertical Angles
    • When 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 4 2 Angles 1 & 2 are vertical angles and 3&4 are vertical angles.
  • 21. GUIDED PRACTICE for Example 2 Find the measures of the numbered angles. SOLUTION STEP 1 137° 43° 43° It is given that m 5 = 137 . 5 and 7 are vertical angles.Their measures are equal, so m 7 = 137 ° .
  • 22. GUIDED PRACTICE for Example 2 Find the measures of the numbered angles. SOLUTION STEP 1 54° 126° 126° It is given that m 8 = 54 . 8 and 10 are vertical angles. Their measures are equal, so m 10 = 54 ° .
  • 23. Homework
    • Page 406 #1-11