This document defines and describes different types of angle relationships: adjacent angles share a vertex and side; vertical angles are nonadjacent angles formed by two intersecting lines and are congruent; a linear pair are adjacent angles with noncommon opposite rays; complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees; and perpendicular lines intersect to form four right angles and congruent adjacent angles.

1. 1.5 Angle Relationships

2. Objective Identify and use special pairs of angles. Identify Perpendicular lines.

3. Adjacent Angles Adjacent angles are two angles that lie in the same plane, have a common vertex and a common side, but no common interior points.

4. Vertical Angles Vertical Angles are two nonadjacent angles formed by two intersecting lines.

5. Vertical Angles Vertical Angles are congruent.

6. Linear Pair A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays.

7. Example Name two angles that form a linear pair, and two acute vertical angles.

8. Angle Relationships Complimentary Angles are two angles with measures that have a sum of 90. Supplementary Angles are two angles with measures that have a sum of 180.

9. Perpendicular Lines 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 the figure indicates that the lines are perpendicular.