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.