Rational vs. Irrational
Construct triangle ABC with A=(0,0), B=(1,0), and C=(0,1). Find the exact length of the hypotenuse. Does segment BC exist? Why or why not?
In "Bridging the Gap... Or not" you did not construct an equilateral triangle. Do rational equilateral triangles exist? Why or why not? Hint: You should answer "why" not "why not."