Points, Lines, Planes
Planes and Space
Tangents and Secants
Chords, Power Point
Congruent Circles, Arcs
Symmetry and Transformations
Rules Postulates Theorems
Angles are a fundamental component of geometry. They are used to determine the amount of difference in the directions of other geometric objects such as lines, rays, line segments and planes.
An angle is usually defined as follows:
Each ray is a side of the angle while the shared endpoint is called the vertex. There are many different types of angles that are classified in different ways. They may be classified by their relation to another angle or where they appear in a geometry figure. The most common way depends on how wide the rays are pointing away from each other.
Angles are measured according to the divisions of the circle called degrees or radians.
A degree can be defined as follows:
The circumference is the length of the outer edge of the circle while the area is inside.
The degree is the most common unit of measurement for angles and is used to classify three fundamental types of angles. The symbol for a degree is °.
The acute angle is an angle whose degree measure is less than 90°.
The right angle always has a measure of 90°. An object in geometry that is 90° to another is said to be perpendicular.
An angle that is more than 90° is said to be an obtuse angle. Usually, this angle is between 90° and 180°.
A 180° angle is sometimes called a straight angle which is basically just a straight line.
If an angle is greater that 180°, it may be called a reflex angle. It is used in special cases to count the number of degrees clockwise or counter-clockwise from a reference line.
Also, if an angle is 360° then it goes all the way around the circle back to 0°. So 0° and multiples of 360° are the same point on the circle.
Angles of Intersecting Lines
Another type of angle is called a vertical angle. When two lines intersect but in different directions, they create vertical and adjacent angles. The vertical angles are opposite each other while the adjacent angles are next to each other.
Angles That Add To 90° and 180°
The measure of an angle is indicated with the m and the angle symbol together: m.
When two lines intersect the adjacent angles are also supplementary angles.
The vertical angles have the same measure. Also, when two or more angles have the same measure they are called congruent. Therefore, it can be said that vertical angles are congruent.
In addition to being called supplementary angles, if the angles themselves share a side but still add to 180° then they are called a linear pair.
If an angle is split in two by a geometric object such as a line, ray or plane then the object is called the bisector if the two resulting angles are congruent. In other words, equal in measure.
Bisectors also exist for other geometric objects such as line segments.
Point notation is often used to describe a particular angle.
Sometimes the letter representing the vertex is used such as P but if there are three points in the angle with one at the vertex then all three points are used in the label such as OPQ where the letter for the vertex would be in the middle.
Some of the postulates for angles include the following:
Points, Lines, Planes
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