## Constructing an equilateral triangle given one side

**How to construct an equilateral triangle given one side**

**The theory behind how it works**

**Constructing an Equilateral Triangle given one side AB**

- By setting your compass to radius AB and swinging two arcs from Point A and point B, you will create point C.
- Join point A to C and B to C. This will create an Equilateral triangle.

**Proof:**

- Line segment AB, AC and CB are congruent as they are all drawn with the same compass width.
- Triangle ABC is an equilateral triangle as it has three sides of equal length.

**Note:**

- When you swing the radius AB, the arcs will intersect in two places if you draw almost a full circle. By joining A and B to either point of intersection will create an equilateral triangle.
- Also this principle of construction will work regardless of the size or angle of the line you start with.