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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 Click the mouse button or press the Space Bar to display the answers. Lesson 2-1 Inductive Reasoning and Conjecture Lesson 2-2 Logic Lesson 2-3 Conditional Statements Lesson 2-4 Deductive Reasoning Lesson 2-5 Postulates and Paragraph Proofs Lesson 2-6 Algebraic Proof Lesson 2-7 Proving Segment Relationships Lesson 2-8 Proving Angle Relationships Example 1 Angle Addition Example 2 Supplementary Angles OBJECTIVE: To write proofs involving supplementary and complementary angles (2.9.8J) (M8.D.1.1) KEY CONCEPT: POSTULATE 2.10 Protractor Postulate • Given AB and a number r between 0 and 180, there is exactly one ray with endpoint A, extending on either side of AB , such that the measure of the angle formed is r. KEY CONCEPT: POSTULATE 2.11 Angle Addition Postulate • If R is in the interior of PQS, then mPQR + mRQS = mPQS. • If mPQR + mPQS, then R is in the interior of PQS. 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. 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? 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 . 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. QUILTING The diagram below shows one square for a particular quilt pattern. If and is a right angle, find Answer: 50 If and form a linear pair and find Supplement Theorem Subtraction Property Answer: 14 If and find . Answer: 28 are complementary angles and 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? 6 = 43 and 7 = 90 2. If m11 = x – 4, m12 = 2x – 5, and 11 and 12 are supplementary, what is the measure of 11 and 12? 11 = 59 and 12 = 121 End of Custom Shows WARNING! Do Not Remove This slide is intentionally blank and is set to auto-advance to end custom shows and return to the main presentation.