How does the cat guess your triangle's type? How could you write a program to guess a quadrilateral or other shape? The key to remixing this program is using a binary tree--each question you ask splits the possible answers into two groups. "Which questions are important?" That's the first important thing to ask!
This program is an extension of the Mystery Shapes game in The Architects' Project by Sylvia Glassco and Catherine Twomey Fosnot.