Another successful experiment getting my participation-
challenged geometry class to interact with each other yesterday.
Each student received a cut-out triangle from the image at left.
The challenge: One (or possibly two) people in this room have
triangles similar to yours. Your task is to find the person and
do the following: - Find the similarity ratio between your
triangle and your match in the order big:small. - Determine the
ratio of the perimeters of each of your triangles. - Determine
the ratio of the areas of each of your triangles. I then cut
them loose. Almost immediately they started scrambling around
the classroom holding up triangles and calculating as quickly as
possible. (I didn’t totally get why they were in a hurry,
actually.) They clustered on tables and rapidly shifted partners
until everyone found they were in the right place. The
calculating began for perimeter – that was the easy part. Then
the area question took center stage. Some asked me how to find
the heights of the triangles, and I