Creating two circles with the same radius will create one side of the triangle. One of the circles will have A as its center and B on the edge of the circle. The other circle will have B as its center and A on the edge of the circle. The intersection point of the two circles is the third vertex of the triangle. This side is the radius of both circles.

Click on the different parts of the construction and see if the triangle continues to be an equilateral triangle.