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Transcript
June 20, 2013 Geometry 1-5 Angle Relationships Angles have many special relationships. We will look at a few of these relationships today. Two angles that lie in the same plane, share a common side and a common vertex are called adjacent angles. Angles that do not fit this discription are called nonadjacent angles. 1 2 Angles 1 and 2 are adjacent. Complementary angles are two angles with measures that add up to 90. 3 4 Angles 3 and 4 are nonadjacent. Supplementary angles are two angles with measures that add up to 180. Two special relationships to be aware of: Vertical angles are congruent. The angles in a linear pair are supplementary. A linear pair of angles are two adjacent angles whose noncommon sides form a straight line. Vertical angles are nonadjacent angles formed by intersecting lines. 1 2 Angles 1 and 2 are a linear pair. 1 3 4 2 Angles 1 and 4 are vertical angles; angles 2 and 3 are vertical angles. Find the measures of two supplementary angles if the difference in their measures is 18. x + y = 180 x - y = 18 2x = 198 x = 99 99 + y = 180 y = 81 The two angles are 99 and 81. June 20, 2013 x + y = 90 x = 2y + 12 2y + 12 + y = 90 3y + 12 = 90 3y = 78 y = 26 Lines, segments, and/or rays which intersect at right angles are called perpendicular . The symbol for this is . T Find the measures of two complementary angles if the larger angle is 12 degrees more than twice the smaller angle. T PAUSE HERE AND TRY THIS ONE. Find values for x and y so that PR SQ. x + 26 = 90 x = 64 R 4y - 2 The two angles are 64 and 26. Sometimes we can assume things from a diagram; other times, we cannot make assumptions. CAN ASSUME Points that appear coplanar are coplanar. Points that lie on a line togethre are collinear. Lines that appear to intersect do intersect. Points appear in the order shown. Points that appear to be interior to an angle are interior; those that appear to be exterior are exterior. Angles that appear adjacent are adjacent; those that appear to be a linear pair are a linear pair. S 2x P 5x + 6 Q 2x + 5x + 6 = 90 7x + 6 = 90 7x = 84 x = 12 4y - 2 = 90 4y = 92 y = 23 CANNOT ASSUME We cannot assume lines are perpendicular. We cannot assume segments are congruent. We cannot assume angles are congruent. We cannot assume relative sizes of angles or segments.