# 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.