That the internal angles of a triangle on the Euclidean plane add up to pi, can be derived directly, without resorting to proof by contradiction. (Hint: Draw a

That the internal angles of a triangle on the Euclidean plane add up to pi, can be derived directly, without resorting to proof by contradiction. (Hint: Draw a parallel line to one of the edges, which passes through the vertex not contained in that edge.) Also, a proof by contradiction of an equality is unsatisfactory in constructive mathematics, because, in general, you can't go from “that A and B are not equal implies a contradiction” to “A and B are equal”. (This would require equality to be decidable.)