Introduction to Geometry
Basic Geometric Elements
The Building Blocks of Geometry
Everything in geometry is built from a few simple ideas. Once you understand these core components, you can start to see how they fit together to create the complex shapes and figures we see all around us. The most basic of all is the point.
Point
noun
A specific location in space, having no size, dimension, or shape.
A point is just a dot. It marks a position, but it has no length, width, or height. Think of it as a single coordinate on a map. We usually represent points with a capital letter.
If you string an infinite number of points together in a straight path, you get a line.
Line
noun
A straight, one-dimensional figure that has no thickness and extends endlessly in both directions.
A line is perfectly straight and goes on forever. Because we can't draw something that's infinitely long, we show a line with arrows on both ends to signal that it keeps going.
Pieces of a Line
Since lines go on forever, we often work with specific pieces of them. Two common types are line segments and rays.
Segment
noun
A part of a line that is bounded by two distinct end points, and contains every point on the line between its end points.
A line segment has a clear beginning and a clear end. Unlike a line, it has a specific length that you can measure. We name a line segment by its two endpoints, like segment .
What if you take a piece of a line that has a starting point but no end point? That's called a ray.
Ray
noun
A part of a line that starts at a particular point and extends infinitely in one direction.
A ray has one endpoint (its starting point) and continues forever in the other direction. We show this with a point at one end and an arrow at the other.
When Rays Meet
When two rays share the same endpoint, they form an angle. The shared endpoint is called the vertex, and the two rays are called the sides of the angle. We measure angles in degrees ().
Angles are all about the amount of turn or rotation between the two rays.
There are three basic types of angles you'll encounter most often.
A right angle is exactly 90°. It's the corner of a square or a perfectly upright 'L' shape. We mark it with a small square at the vertex.
An acute angle is any angle that measures less than 90°. The word 'acute' can mean sharp, and these angles look pointy.
An obtuse angle measures more than 90° but less than 180°. These angles are wider and more open than right angles.
Time to check your understanding of these fundamental building blocks.
Which of the following best describes a point in geometry?
A straight path that has two distinct endpoints and a measurable length is called a...
These five elements—points, lines, segments, rays, and angles—are the alphabet of geometry. Everything else is just a combination of these simple parts.