1. Measures and Relationships
Angles
Measures and Relationships

2. 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

3. 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.

4. 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

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

6. 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

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

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

9. 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

10. 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

11. Interpreting Diagrams

12. 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?