1. 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.

2. 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.

3. Example 5-1c Name an angle pair that satisfies each condition. a. two acute vertical angles b.two adjacent angles whose sum is less than 90 Answer:  BAC and  CAD or  EAF and  FAN Answer:  BAC and  FAE,  CAD and  NAF, or  BAD and  NAE

4. 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.

5. Example 5-2d 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

6. 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.

7. Example 5-3c ALGEBRA Find x and y so that and are perpendicular. Answer:

8. Determine whether each statement can be assumed from the figure below. Explain. a. b.  TAU and  UAY are complementary. c.  UAX and  UXA are adjacent. Example 5-4d Answer: Yes; lines TY and SX are perpendicular. Answer: No; they do not share a common side. Answer: No; the sum of the two angles is 180, not 90.