+1206 How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a \(4 * 4\) square array of dots like the one shown below?
dot((0,0));dot((0,1));dot((0,2));dot((0,3));
dot((1,0));dot((1,1));dot((1,2));dot((1,3));
dot((2,0));dot((2,1));dot((2,2));dot((2,3));
dot((3,0));dot((3,1));dot((3,2));dot((3,3));
Two triangles are congruent if they have the same traced outline, possibly up to rotating and flipping. This is equivalent to having the same set of 3 side lengths.
