## Dividing a Line into an Equal Amount of Parts

**How to divide a line into a certain amount of parts**

**What You Start With**

Shown above is a line of any length and any angle. Before you start you will have to know how many parts you want the line divided up into.

**The Theory Behind How it Works**

Above is the given the line divided into 5 equal parts. This construction is based heavily on the principles of similar triangles. See the section on similar triangles if you are unsure on what similar triangles are.

- Draw a line at any angle from point A or B (it doesn't matter which one you choose) any length, represented by the green line above.
- Depending on the question mark off the required amount of steps using your compass, using the same radius. In the question we are required to divide into 5 equal parts, so step off 5 arcs.
- Join the fifth arc back to point B. this creates a triangle.
- Finally bring lines form the remaining 4 arcs parallel to line B5. Where these lines meet line AB divide into 5 equal parts.
- These 4 new line help create 4 new triangles. This principle works because all 5 triangles created are similar. Each triangle has the same 3 angles and because the 5 arcs we drew at the start were in the same ratio.