Below are some of the key concepts and terms you will need to know in order to begin your study of geometry.
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.
Points A, B, and C
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.
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 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.
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.
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!
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 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 .
If extended infinitely, the lines above will never meet.
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.
In both figures, the red line is a transversal.
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 is the set of all possible points on an infinite number of planes. Thus, space covers all three dimensions - length, width, and height.