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
Proof:
Note:
- 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.