Starting point from @CmonMattTHINK

The questions linked to above could probably be introduced in a friendlier context, as opposed to being apropo of nothing. For example,

"An artist friend is creating a large mosaic out of ceramic triangles, and asks you to make the triangles for her. Below are the specifications for the kinds of triangles she would like you to make. She wants you to let her know if you have any questions for her."

The hope is that, for the descriptions where only one triangle is possible, little will be said. Where no triangles are possible, the students should say so. What might be difficult is getting them to notice when more than one triangle is possible. They might find that one triangle is possible, and be satisfied with that.

Matt E (@CmonMattTHINK)