Can you draw a right angled equilateral triangle?

No. That can be proven in this way, accepting the truth of the Pythagorean Theorem, which says that the square of the length of the hypotenuse, c, of a right triangle with orthogonal sides a and b, will always be equal to the sum of the squares of the lengths of sides a and b. If c is the length of side c, and so on, the Pythagorean Theorem stated above becomes this mathematical statement: c2 = a2 + b2 One way to test a hypothesis is to express the assumed case, apply logic steps to it, and examine the truth of the result. So if we assume for argument that our right triangle is equilateral, and assign length xequally to all three sides--a, b, & c--we could write the equation thus: x2 = x2 + x2 which becomes x2 = 2(x2) Factoring out x2, we get 1 = 2 We've arrived at a mathematical contradiction, disproving our assumption. There cannot be right-angled equilateral triangles.