My son and I were trying to decide whether an isosceles triangle can ever have 90 degree base angles. I would argue that if the two equal length sides are both infinitely long, they must have 90 degree angles, because any angle less than 90 degrees would result in a side that is not infinitely long. My son on the other hand argued that in this case it is not a triangle because the angles of a triangle have to add up to 180 degrees. My husband added that if the angles are 90 degrees the lines would not be touching, even at infinity.
Who's right?
Best Answer
I agree with your son, but with a slightly different argument. I my mind it doesn't make sense to talk about a triangle with infinitely long sides. (In the projective plane you could define it, but I don't see the point).