Basic Geometry Terms

Below are some of the key concepts and terms you will need to know in order to begin
your study of geometry.

Points

In geometry, we use points to specify exact locations. They are generally denoted
by a number or letter. Because points specify a single, exact location, they are
zero-dimensional. In other words, points have no length, width, or height. It may
be helpful to think of a point as a miniscule “dot” on a piece of paper.

Three geometric points labeled A, B, and C

Points A, B, and C

Lines

Lines in geometry may be thought of as a “straight” line that can be drawn on paper
with a pencil and ruler. However, instead of this line being bounded by the dimensions
of the paper, a line extends infinitely in both directions. A line is one-dimensional,
having length, but no width or height. Lines are uniquely determined by two points.
Thus, we denote the name of a line passing through the points A and
B as
, where the two-headed arrow signifies that
the line passes through those unique points and extends infinitely in both directions.

An infinitely extending line with two points, labeled A and B

Line Segments

Consider the task of drawing a “straight” line on a piece of paper (as we’ve done
when thinking about lines). What you’ve actually done is create a line segment.
Because our piece of paper has defined dimensions and we cannot draw a line infinitely
in any direction, we have constructed a segment that begins somewhere and ends somewhere.
We write the name of a line segment with endpoints A and B
as
. Note that the notation for lines and
line segments differ because a line segment has a defined length, whereas a line
does not.

A line segment with two endpoints labeled A and B

Rays

A ray is a “straight” line that begins at a certain point and extends infinitely
in one direction. A ray has one endpoint, which marks the position from where it
begins. A ray beginning at the point A that passes through point
B
is denoted as
. This notation shows that the ray begins at
point A and extends infinitely in the direction of point B.

A ray that extends infinitely in one direction, beginning at point A with another point labeled B

Endpoints

Endpoints mark the beginning or end of a line segment or ray. Line segments have
two endpoints, giving them defined lengths, whereas rays only have one endpoint,
so the length of a ray cannot be measured.

Midpoints

The midpoint of a line segment marks the point at which the segment is divided into
two equal segments. In other words, the lengths of the segments from either endpoint
to the midpoint are equal. For instance, if M is the midpoint of the
segment
, then
. Note that neither lines nor rays
can have midpoints because they extend infinitely in at least one direction. It
would be impossible to find the middle of a line or ray that never ends!

A line segment with endpoints labeled A and B, and a midpoint labeled M

Intersection

When we have lines, line segments, or rays that meet, or cross at a certain point, we call
it an intersection point. In other words, those figures intersect somewhere.

Two lines intersecting, with an intersection point labeled E

Parallel

Two lines that will never intersect are called parallel lines. In the case of line
segments and rays, we must consider the lines that they lie in. In other words,
we must consider the case that the line segments or rays were actually lines that
extend infinitely in both directions. If the lines they lie on never intersect,
they are called parallel. For instance, the statement “
is parallel to
,” is expressed mathematically as
.

Two parallel lines with points labeled A, B, C, and D

If extended infinitely, the lines above will never meet.

Transversal

A transversal is a type of line that intersects at least two other lines. The
lines that a transversal crosses may or may not be parallel.

Two examples of transversals highlighted red, intersecting parallel and non-parallel lines

In both figures, the red line is a transversal.

Planes

A plane can be thought of as a two-dimensional flat surface, having length and width,
but no height. A plane extends indefinitely on all sides and is composed of an infinite
number of points and lines. One way to think about a plane is as a sheet of paper
with infinite length and width.

Space

Space is the set of all possible points on an infinite number of planes. Thus, space
covers all three dimensions – length, width, and height.

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