1. How many different non-congruent isosceles triangles can be formed by connecting three of the dots in a square array of dots like the one shown below?
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.
2. I have $5$ different pullover shirts and $4$ different button-down shirts. In how many ways can I choose shirts for the next $9$ days if I insist on wearing pullover shirts two days in a row at least once? Assume that I wear one shirt each day, and every shirt gets worn once.