What is “Geometry?”

Geometry is defined as “a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids.”*

Put simply, geometry is a type of math that deals with points, lines, shapes, and surfaces. When you hear “geometry,” thoughts of shapes, area, and volume probably come to mind—and that is precisely what geometry is!

Geometry, just like algebra, is built on a mathematical ruleset. In geometry**, we refer to these rules as axioms, and there are 5 big ones that you should know.

What are the 5 axioms of geometry?

1. A straight line can be drawn between any two points.

Any two points in the same plane, or same flat space, can be connected by a straight line. This axiom is a fancy way of saying that you can “connect the dots.”

2. A straight line can be extended indefinitely.


Straight lines can go on and on—to infinity & beyond!

3. A circle can be made using any point as its center and a line segment as its radius.

This axiom says that you can make a circle around any point in a plane. Its radius will extend from the dot to the edge of the circle, forming a straight line.

4. All right angles are congruent.


We’ll cover congruence in another post, but for now, this just means that all right angles are the same. All right angles are exactly 90 degrees—no more, no less.

5. Parallel Postulate: given a straight line and a point (not on the line), there is always a second straight line through the point that will be parallel to the first line.

This one is a little less intuitive—pictures like the above help to clarify the statement. Essentially, this postulate just means that we can always draw a second line parallel to another line, assuming they’re in the same plane.

Many other theorems and properties can be built from these 5 axioms, just like how rules and equations are built on each other in algebra. Consider these 5 axioms your geometric foundation for more complex problems down the line.

Need to ask a question about geometry, but don’t know where to go? UPchieve’s here to help. Connect with a tutor right now—it’s easier than saying Parallel Postulate three times fast!

* Source: https://www.merriam-webster.com/dictionary/geometry. 

** Here we are referring to Euclidean Plane Geometry, which is the standard type of geometry taught in high school mathematics.