Aki introduced us to a specific problem on a 7 X 7 geoboard. See 7x7geoboard.doc. Two points were labeled. Calling the bottom left peg (1, 1), A had coordinates (3, 2) and B had coordinates (6, 3). Segment AB was drawn. The instruction was to find all of the isosceles triangles that could be made with AB as a side. We worked on this in groups and came up with nine distinct solutions. Aki helped us categorize them in terms of which pair of sides were congruent. See Solutions to Isosceles Triangle Problem.
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.