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Transcript
Angle Relationships Adjacent - Two angles are adjacent if and only if they satisfy four conditions: 1. They lie in the same plane. 2. They have a common vertex. 3. They have a common side. 4. They have no common interior points. Angle Relationships Vertical angles - Two nonadjacent angles formed by two intersecting lines. All vertical angles are congruent. Linear Pair - A pair of adjacent angles whose noncommon sides are opposite rays. The angles in a linear pair have measures that add to 180 degrees. Name an angle pair that satisfies each condition. a. two acute vertical angles Answer: BAC and FAE, CAD and NAF, or BAD and NAE b. two adjacent angles whose sum is less than 90 Answer: BAC and CAD or EAF and FAN Angle Relationships Complementary Angles - Two angles whose measures have a sum of 90 degrees. Supplementary Angles - Two angles whose measures have a sum of 180 degrees. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other. Answer: 16, 74 Angle Relationships Perpendicular () - Lines that intersect to form right angles. • Perpendicular lines intersect to form four right angles. • Perpendicular lines intersect to form congruent adjacent angles. • Segments and rays can be perpendicular to lines or to other line segments and rays. • The right angle symbol in a figure indicates that the lines are perpendicular. ALGEBRA Find x and y so that are perpendicular. Answer: and Determine whether each statement can be assumed from the figure below. Explain. a. Answer: Yes; lines TY and SX are perpendicular. b. TAU and UAY are complementary. Answer: No; the sum of the two angles is 180, not 90. c. UAX and UXA are adjacent. Answer: No; they do not share a common side.