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# 8.1 angles 1

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### 8.1 angles 1

1. 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. 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. 3. Chapter 8.1 Lines and Angles
4. 4. Essential Questions <ul><li>Why is it important to be able to identify congruent triangles in everyday life? </li></ul><ul><li>Where in real life can you use the properties of isosceles and equilateral triangles? </li></ul><ul><li>How are the relationships between lines and planes used in the real world? </li></ul><ul><li>What areas in the real world are properties of parallel lines important? </li></ul>
5. 5. Chapter 8 Section 1 <ul><li>Vocabulary 1-14 </li></ul>
6. 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. 7. <ul><li>Plane : A flat surface that extends without end. </li></ul><ul><li>Angle: a figure formed by two rays that begin at a common point called the vertex. </li></ul>Vertex Vertex: end point of the rays that form an angle. C A B
8. 8. <ul><li>Degree: unit of measure. 95 0 </li></ul>
9. 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. 10. Classifying Angles <ul><li>Angles are classified by degrees. </li></ul><ul><li>Acute - greater than 0 degrees but less than 90 degrees. </li></ul>C A B This is read “Angle ABC or Angle CBA, or just Angle B
11. 11. Classifying Angles <ul><li>Obtuse – angles measuring more than 90 degrees but less than 180 degrees. </li></ul>
12. 12. Classifying Angles <ul><li>Right Angles measure exactly 90 degrees and labeled with “square” in the corner of the angle. </li></ul>
13. 13. Classifying Angles <ul><li>A straight angle “looks like” a straight line, but it actually is an angle. It measures exactly 180 degrees. </li></ul>A B C
14. 14. <ul><li>Two angles are complementary if the sum of their measures is 90 degrees. </li></ul>70 ° 20 ° 70 + 20 = 90 degrees.
15. 15. <ul><li>Are these complementary angles? </li></ul>60 ° 30 °
16. 16. <ul><li>Two angles are supplementary if the sum of their measures is 180 degrees. </li></ul><ul><li>2 </li></ul>
17. 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. 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. 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. 20. Vertical Angles <ul><li>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. </li></ul>1 3 4 2 Angles 1 & 2 are vertical angles and 3&4 are vertical angles.
21. 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. 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. 23. Homework <ul><li>Page 406 #1-11 </li></ul>