Consider the right triangle as half of a rectangle where the diagonal of the rectangle is the hypotenuse of the right triangle. If the other diagonal of the rectangle is drawn it intersects at the centre of the rectangle and the two diagonals bisect one another. If two perpendiculars from this central point are made from this point to the length side and the width side of the rectangle, we can see that these perpendiculars are the perpendicular bisectors of the right triangle. So we know that they meet on the diagonal exactly half way along, which is the centre of the rectangle. Half way along the diagonal is the same as half way along the hypotenuse.
