ANGLES – RECOGNIZING FIGURES

Concept: A line is a path of points that extends in two opposite directions and has no endpoints. A line segment is a part of a line which has two endpoints. A ray has one endpoint and a path of points that extend in one direction away from the endpoint. An angle is formed by two rays that have a common endpoint. In the first illustration below, angle DMB is formed by two rays, ray MD and ray MB. The common endpoint is M. Point M is also called the vertex of the angle. Ray MD and ray MB are the sides of the angle.

Angles may be named in several ways:

1. Angles may be named by using three letters, as in the diagram below.

2. An angle may be named with only one letter, placed at the vertex.

3. An angle may be named by placing a small letter or number near the vertex and between the rays.

Angles are classified by their size. A right angle is an angle that is formed by perpendicular rays. An acute angle is an angle that is smaller than a right angle. A straight angle is an angle that forms a straight line. An obtuse angle is an angle that is smaller than a straight angle, but larger than a right angle. A reflex angle is an angle that is larger than a straight angle, but smaller than 360 degrees.

ANGLES DEFINITION CHART
name | definition | symbol | figure
Line | A line is a path of points that extends in two opposite directions and has no endpoints. | Line MN is written ↔ MN |
Line segment | A line segment is a part of a line which has two endpoints. | Line segment PQ is written |
Ray | A ray is a part of a line, which has one endpoint. | Ray BG is written → BG |
Straight angle | A straight angle is an angle that forms a straight line. | Angle A is written |
Obtuse angle | An obtuse angle is an angle that is smaller than a straight angle, but larger than a right angle. | Angle B is written |
Right angle | A right angle is an angle that is formed by perpendicular (90 degree) rays. | Angle R is written |
Reflex angle | A reflex angle is an angle that is larger than a straight angle, but smaller than 360 degrees. | Angle P is written |
Acute angle | An acute angle is an angle that is smaller than a right angle. | Angle V is written |
Complementary angles | Complementary angles have two angles whose sum is 90 degrees. | In the figure on the right, angles 1 and 2 are complementary angles. |
Supplementary angles | Supplementary angles have two angles whose sum is 180 degrees. | In the figure on the right, angles 1 and 2 are supplementary angles. |
Vertical angles | Vertical angles are formed when two straight lines cross at a point. Vertical angles lie across from each other and are equal. | In the figure on the right, angles 1 and 3 are vertical angles, as are angles 4 and 2. |