Angle Pairs
Complementary and Supplementary Angles
Special names are given to pairs of angles whose sums equal either 90 or 180 degrees. A pair of
angles whose sum is 90 degrees are called complementary angles. Each angle is the other angle's
complement.
Dimension
Dimension is a characteristic of all geometric regions, objects, and spaces. The previous sections
have probably already made you aware of the concept of dimension. It is roughly the number of
directions in which a region or object can be measur
Parallel Lines
Because lines extend infinitely in both directions, every pair of lines either intersects once, or don't
intersect at all. The pairs of lines that never intersect are called parallel lines. Although parallel lines
are usually thought of in
Dividing Angles and Segments
Dividing Angles
Angles can be divided just like ordinary numbers. An angle can only be divided by a ray on the
interior of the angle, though. Such a ray that divides an angle into two equal angles is called an
angle bisector.
Lines
Lines
A line is the infinite set of all points arrayed in a straight formation. It is difficult to formally define, but
easy to understand. A line has no thickness; it has only length, and can be named by any two points
on that line. For example, a
Angles
An angle is a geometric figure consisting of two rays with a common endpoint. It looks like this:
Figure %: Angle ABC
The common endpoint is called the vertex of the angle; in this case the vertex
is point A, which is a part of the ray AB as well a
Planes
A plane is a boundless surface in space. It has length, like a line; it also has width, but not thickness.
A plane is denoted by writing "plane P", or just writing "P". On paper, a plane looks something like
this:
Figure %: Plane P
There are two wa
Perpendicular Lines
Lines (or segments) are called perpendicular if their intersection with one another forms a right
angle. You can see for yourself that if one of the angles formed by the intersection of two lines or
segments is a right angle, then all
Space
So far we have dealt with points, lines, and planes. All of these lie within space. Space is the
collection of all points. It has no shape, and it has no limits. Space is three-dimensional; that is, it has
length, width, and a new dimension, height.
Terms
Acute Angle - An angle whose measure is less than 90 degrees.
Adjacent Angle - Angles that share a vertex, one side, and no interior points.
Alternate Exterior Angles - Angles created when a transversal intersects with two lines. Alternate
exterior