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Unit #1, Concept #3 Angles and their Measurements

Unit #1, Concept #3 Angles and their Measurements. What are angles and how are they classified? How are the measures of angles used to determine their congruency? What is angle addition and how is it used?. Bell Ringer. With your partner…

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Unit #1, Concept #3 Angles and their Measurements

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  1. Unit #1, Concept #3Angles and their Measurements • What are angles and how are they classified? • How are the measures of angles used to determine their congruency? • What is angle addition and how is it used? Free Template from www.brainybetty.com

  2. Bell Ringer With your partner… Come up with a list of some things that you remember about angles. Free Template from www.brainybetty.com

  3. An angle ( ) • Is formed by two rays with the same endpoint. • The two rays are the sides of the angles. The endpoint is called the vertex of the angle Free Template from www.brainybetty.com

  4. Naming Angles • 1 • Naming Angles C B A Free Template from www.brainybetty.com

  5. Postulate 1 – 7Protractor Postulate • OA is paired with 0 and OB is paired with 180. • If OC is paired with x and OD is paired with y, then m<COD = |x – y|. D C y x A B Free Template from www.brainybetty.com

  6. Find the measure of BOD D C A B Free Template from www.brainybetty.com

  7. Find the measure of AOD D C A B Free Template from www.brainybetty.com

  8. Types of Angles • Acute angles - an angle whose measure is between 0º and 90º. • Right angle - an angle whose measure is 90º. • Obtuse angle - an angle whose measure is between 90º and 180º. • Straight angle - an angle whose measure is 180º Free Template from www.brainybetty.com

  9. Classify each angle AOY • as right, acute, obtuse or straight. Y X Z A B Free Template from www.brainybetty.com

  10. Classify each angle BOY • as right, acute, obtuse or straight. Y X Z A B Free Template from www.brainybetty.com

  11. Classify each angle BOA • as right, acute, obtuse or straight. Y X Z A B Free Template from www.brainybetty.com

  12. Classify each angle XOZ • as right, acute, obtuse or straight. Y X Z A B Free Template from www.brainybetty.com

  13. Find the measure of the followingAOX, XOY, YOZ, XOZ, YOB Y X Z A B Free Template from www.brainybetty.com

  14. Let’s Get it Started • What did the segment addition postulate state? Free Template from www.brainybetty.com

  15. Postulate 1 – 8 Angle Addition Postulate • If point B lies in the interior of AOC, then • m AOB + m BOC = m AOC. • C • B • O • A Free Template from www.brainybetty.com

  16. Using the Angle Addition Postulate • m AOB = 54 • m AOC = 76 Find m BOC. C B O A Free Template from www.brainybetty.com

  17. Using the Angle Addition Postulate • m COB = 2x + 6 • m AOB = 5x – 11 and m AOC =79 C B O find x A Free Template from www.brainybetty.com

  18. Using the Angle Addition Postulate • Find the measure of angle 1 153° 1 Free Template from www.brainybetty.com

  19. Using the Angle Addition Postulate • Find the value of x. (3x + 5)° (9x + 7)° Free Template from www.brainybetty.com

  20. Congruent Angles • Are angles with the same measure. 1 2 Free Template from www.brainybetty.com

  21. What can you deduce from this diagram? • A D • B E • C Free Template from www.brainybetty.com

  22. What can you deduce from this diagram? • A D • B E • C Free Template from www.brainybetty.com

  23. Journal Entry • What are angles and how are they classified? • 2. How are the measures of angles used to determine their congruency? • 3. What is angle addition and how is it used? Free Template from www.brainybetty.com

  24. Classwork/Homework • Page 30 – 32 • # 17 – 23 odd, 24 – 28 all, 47, 48, 56-67, 70, 75 Free Template from www.brainybetty.com

  25. Unit #1, Concept #3Angles and their Measurements • What are angles and how are they classified? • How are the measures of angles used to determine their congruency? • What is angle addition and how is it used? Free Template from www.brainybetty.com

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