3-3 Adjacent and Vertical Angles A basic property of angles is that the measure of an angle formed by the outside rays of adjacent angles is the sum of.

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Presentation transcript:

3-3 Adjacent and Vertical Angles A basic property of angles is that the measure of an angle formed by the outside rays of adjacent angles is the sum of the measures of the adjacent angles.

3-3 Adjacent and Vertical Angles Two nonstraight and nonzero angles are adjacent angles if and only if a common side is in the interior of the angles formed by the noncommon sides.

3-3 Adjacent and Vertical Angles VR is the angle bisector of  PVQ if and only if VR (except for point V) is in the interior of  PVQ and m  PVR = m  RVQ. V P R Q 50 o

3-3 Adjacent and Vertical Angles Angle Measure Postulate –Angle Addition Assumption If angles AVC and CVB are adjacent angles, then m  AVC + m  CVB = m  AVB. A C B V

3-3 Adjacent and Vertical Angles If the measures of two angles are r and s, then the angles are: complementary angles iff r + s = 90; supplementary angles iff r + s = 180. A B C

3-3 Adjacent and Vertical Angles Equal Angle Measures Theorem If two angles have the same measure, their complements have the same measure. If two angles have the same measure, their supplements have the same measure.

3-3 Adjacent and Vertical Angles Two adjacent angles of a linear pair if and only if their noncommon sides are opposite rays. A B C D

3-3 Adjacent and Vertical Angles Linear Pair Theorem If two angles form a linear pair, then they are supplementary. A B C D

3-3 Adjacent and Vertical Angles Two nonstraight angles are vertical angles if and only if the union of their side is two lines

3-3 Adjacent and Vertical Angles Vertical Angle Theorem If two angles are vertical angles, then their measures are equal

3-3 Adjacent and Vertical Angles Tell why the indicated angles of these figures are not adjacent. a.  A and  C b.  1 and  2 A B C 1 2 J K M L

3-3 Adjacent and Vertical Angles What is m  GKL? What is m  JKL? J L K G I 60 o 50 o 90 o

3-3 Adjacent and Vertical Angles Suppose you are give two angles M and N such that m  M = m  N. If the measure of a complement of  M equals 18x + 10 and the measure of a complement of  N equals 8x + 30, what is the measure of a supplement of  G?