Argument to showing that an equilateral triangle cannot have a right angle? - Answers

If you have an equilateral triangle ABC, then draw the line from A to D, the mid point of BC. Then in trangles ABD and ACD, AB = AC (equilateral), BD = DC (D is midpoint), and AD is common so these two triangles are congruent and so angle ABD = angle ACD. That is, angle ABC = angle ACB. Similarly the third angle can be shown to be the same. Thus an equilateral triangle is also equiangular. Now, sum of the interior angles of any triangle is 180 degrees. So since sum of three equal angles measures is 180 degrees, they must be 60 degrees each, i.e. NOT 90 degrees so there is no right angle..