Measures and Relationships Angles Measures and Relationships

Vocabulary Ray – part of a line that includes one endpoint and extends infinitely in one direction Opposite rays – rays that share a common endpoint and are collinear Angle – object formed from two noncollinear rays that have a common endpoint. Sides – the rays that form the angle Vertex – the common endpoint of an angle

Angle An angle divides a plane into three parts: On the angle, the interior of the angle, the exterior of the angle Angles are measured in units called degrees; a degree is the result of dividing the distance around a circle into 360 parts.

Types of Angles Acute Angles – measure between 0 and 90 degrees Right Angles – measure exactly 90 degrees Obtuse Angles – measure between 90 and 180 degrees

Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles.

Angle Relationships Adjacent angles – two angles that that lie in the same plane and have a common vertex and a common side, but no common interior points

Angle Relationships Linear Pair – a pair of adjacent angles with noncommon sides that are opposite rays

Angle Relationships Vertical Angles – two nonadjacent angles formed by two intersecting lines Vertical not Vertical

Angle Pair Relationships Vertical angles are congruent Complementary angles – two angles with measures that add to 90 degrees Supplementary angles – two angles with measures that add to 180 degrees

Perpendicular Lines Intersect to form four right angles Intersect to form congruent adjacent angles Segments and rays can be perpendicular to lines or other segments and rays

Interpreting Diagrams

Questions Are there any aspects of life where angles are important? What careers paths make extensive use of angles and angle relationships? In what ways do you use angles?