distance from each other at every point.
In three-dimensional Euclidean space,
these lines also do not intersect, main-
taining a constant separation between
points closest to each other on the two
lines. In analytic geometry, parallel
means those lines with the same slope, as
well as other curves with the same slope
for every xvalue. The symbol for parallel
lines is ||. For example, A|| Bmeans that
line Ais parallel to line B.
What is an angle?
An angle is a major concept in both
geometry and trigonometry. An angle is
formed by two rays that begin at the same point; a straight angleis one in which the
two rays lie on the same line. It can also be described as two planes coming from a
common line.
Angles are named in several ways: a capital letter at its vertex (the common points
for both rays, see illustration, B), a small letter within the angle, a number within
the angle, or by three capital letters (ABC or CBA, with the middle letter representing
the vertex and the other two points the rays). The two rays that form the angle are
called the sides of the angle, such as side BA and side BC.
How are angles measured?
Angles are measured in two major ways: degrees and radians. Similar to degrees on a
temperature scale, degreesin mathematics—especially when discussing angles—are
usually denoted by the symbol °; they are divided into 60 arc minutes, and arc minutes
are divided into 60 arc seconds. The multiples of 60 are thought to be connected to the
Babylonian’s sexagesimal number system (one based on the number 60), in which the
year was composed of 360 days (or 12 months at 30 days each). If the vertex of an angle
and one side are fixed and the other side is rotated about the vertex, it sweeps out a circle
of 360° with each complete rotation. Said another way, a full rotation is 360 degrees.
Radians(denoted as rad) are real numbers represented as an angle; they are the
central angle of a circle determined by two radii and an arc joining them. In degrees, a
radian is about 57.29578 degrees or 180/πdegrees, because a semicircle contains π
radians. For example, π/6 is equal to a 30 degree angle; because a straight angle is π
radians (or 180°), if you divide 180 by 6, (or π/6), it is equal to 30 degrees. Radians are
most often used in probability and statistics, or calculus, especially to obtain the deriv-
ative of trigonometric functions. 173
GEOMETRY AND TRIGONOMETRY
Angle ABC is formed by rays BA and BC linked at
point B.