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Lesson 2.6 notes.notebook September 19, 2011 Lesson 2.6: Definitions and Postulates Involving Angles Angle Review Definition: two rays with a common endpoint INTERIOR Ray/Side Angle Ray/Side Vertex EXTERIOR Opposite Rays when two rays make a straight line with 180 degrees Protractor Postulate Let O be a point on AB such that O is between A and B. Consider OA, OB, and all rays that can be drawn from O on one side of AB. These rays can be paired with the real numbers from 0 to 180 so that 1. OA is paired with 0 and OB is paired with 180. 2. If OP is paired with x and OQ is paired with y, then the number paired with POQ is |x y|. This number is called the measure or degree measure, of POQ 1 Lesson 2.6 notes.notebook September 19, 2011 How can we find m MNO? 80 90 70 M 110 50 100 110 60 100 90 120 80 70 130 120 40 60 130 140 30 140 50 0° 40 150 150 O 30 20 160 160 10 20 170 0 170 10 180 180 0 N R Q Find the m BEC. B 80 90 110 60 110 50 100 90 80 70 130 140 50 130 140 30 120 60 120 40 C 100 70 0° 40 150 30 150 160 20 20 160 10 0 R 10 170 0 180 E 170 180 Q 2 Lesson 2.6 notes.notebook September 19, 2011 Types of Angles Acute greater than 0 and less than 90 Right equal to 90 Obtuse greater than 90 and less than 180 Straight equal to 180 Complementary Angles two angles that add up to 90 degrees 38 25 each angle is the complement of the other 65 Supplementary Angles 52 two angles that add up to 180 degrees each angle is the supplement of the other 23 157 61 119 3 Lesson 2.6 notes.notebook September 19, 2011 Adjacent Angles two angles in the same plane that share a common side and a common vertex Linear Pair two adjacent angles that are supplementary What is the difference between supplementary angles and a linear pair? Angle Addition Postulate If point B is in the interior of angle AOC, then m AOB + m BOC = m AOC A B C O 4 Lesson 2.6 notes.notebook September 19, 2011 Find m PRQ. Q n + 2 2n 17 P R T Find m JMK and m KML. J K 2r + 6 60 r M L 5 Lesson 2.6 notes.notebook September 19, 2011 Congruent Angles angles that are equal in measure Angle Bisector a line, segment, or ray that divides an angle in half Homework p. 9697 #2139 All #4348 All 6