2. Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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6. Contents Lesson 2-1Inductive Reasoning and Conjecture Lesson 2-2Logic Lesson 2-3Conditional Statements Lesson 2-4Deductive Reasoning Lesson 2-5Postulates and Paragraph Proofs Lesson 2-6Algebraic Proof Lesson 2-7Proving Segment Relationships Lesson 2-8Proving Angle Relationships

7. Lesson 8 Contents Example 1Angle Addition Example 2Supplementary Angles OBJECTIVE: To write proofs involving supplementary and complementary angles (2.9.8J) (M8.D.1.1)

8. KEY CONCEPT: POSTULATE 2.10 Protractor Postulate Given and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of, such that the measure of the angle formed is r.

9. KEY CONCEPT: POSTULATE 2.11 Angle Addition Postulate If R is in the interior of  PQS, then m  PQR + m  RQS = m  PQS. If m  PQR + m  PQS, then R is in the interior of  PQS.

10. KEY CONCEPT: THEOREMS 2.3 SUPPLEMENT THEOREM: If 2 angles for a linear pair, then they are supplementary angles. 2.4 COMPLEMENT THEOREM: If the noncommon sides of 2 adjacent angles form a right angle, then the angles are complementary angles.

11. Example 8-1a If the second hand stops where the angle is bisected, then the angle between the minute and second hands is one-half the measure of the angle formed by the hour and minute hands, or. TIME At 4 o’clock, the angle between the hour and minute hands of a clock is 120º. If the second hand stops where it bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands?

12. Example 8-1b By the Angle Addition Postulate, the sum of the two angles is 120, so the angle between the second and hour hands is also 60º. Answer: They are both 60º by the definition of angle bisector and the Angle Addition Postulate.

13. Example 8-1b Answer: 50 QUILTING The diagram below shows one square for a particular quilt pattern. If andis a right angle, find

14. Example 8-2a Supplement Theorem Subtraction Property Answer: 14 form a linear pair andfindIfand

15. Example 8-2b Answer: 28 are complementary angles and. andIf find

16. REVIEW 1.If  6 and  8 are complementary,  6,  7, and  8 for a straight line, and  8 = 47, what is the measure of  6 and  7? 2. If m  11 = x – 4, m  12 = 2x – 5, and  11 and  12 are supplementary, what is the measure of  11 and  12?  6 = 43 and  7 = 90  11 = 59 and  12 = 121

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