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An angle essentially corresponds to an “opening” of a geometrical figure, whose quantification leads to much development in geometry and trigonometry. The following table documents some of the most notable symbols related to angles — along with each symbol’s meaning and example.
Common Symbols Used in Geometry. Symbols save time and space when writing. Here are the most common geometrical symbols: Example: In ABC, ∠BAC is ∟. Is really saying: "In triangle ABC, the angle BAC is a right angle" Naming Angles. For angles the central letter is where the angle is. Example: ∠ABC is 45°. The point "B" is where the angle is.
Central Angle = Intercepted Arc. In the diagram at the right, ∠AOB is a central angle with an intercepted minor arc from A to B. m∠AOB = 82º. In a circle, or congruent circles, congruent central angles have congruent arcs. (the converse is also true)
We can measure Angles in Degrees. There are 360 degrees in one Full Rotation (one complete circle around). Angles can also be measured in Radians .
The radian measure of an angle is the ratio of the length of the arc subtended by the angle to the radius of the circle. In other words, if \(s\) is the length of an arc of a circle, and \(r\) is the radius of the circle, then the central angle containing that arc measures \(\frac{s}{r}\) radians.
Equal angles stand on equal chords and vice versa. Equal chords are equidistance from the center and vice versa. The perpendicular bisector of a chord passes through the center of the circle. Any three non-colinear points lie on a unique circle. Tangent-chord theorem. Two secants theorem.
Angles are labeled by specifying 3 points, with the center point being the vertex of the angle. This angle is NOT ∠ BAC . Angles may be labeled with a single letter at the vertex, as long as it is perfectly clear that there is only one angle at this vertex.
