You can construct the equilateral triangle below (with perfect 60[math]^\circ[/math] angles) without using a protractor.[br][br]In plain terms:[br][br]In this worked example, the initial line is drawn using a ruler to an exact length. In this case the line is 6cm long. I now need to draw two small arcs using a compass set to the same distance (of 6cm). From one end of the line I will draw a small arc in the the top middle region above the line. I will then draw another small arc but this time from the other end of the line to the same [top middle] region above the line. This will create an intersect point from where I can draw two more lines to each end of the first line that I drew. This triangle has three perfect 60[math]^\circ[/math] internal angles and each side is of equal length to the others thus making it an equilateral triangle. You can bisect one of the angles to make a 30[math]^\circ[/math] angle.[br][br](Take a look at the dotted lines that represent the [i]path[/i] of the compass. Note that I am [i]not[/i] drawing the entire path of the dotted line. I am drawing the two small arcs only. Don't forget that if you are asked to construct a triangle in this way then ensure that you do [i]not[/i] erase the arcs as this is evidence of your work.)[br][br]Run the graphic below to watch how to construct this equilateral triangle.