prove that all circles are similar

[Cathy Kessel]

Continuing from http://commoncoretools.me/forums/topic/prove-that-all-circles-are-similar/#post-1948

As a preliminary, somewhere in curriculum these ideas could occur in terms of transformations: Can you take any two circles and transform one into the other using rigid motions followed by dilation? And, you could ask it for a variety of things: triangles, equilateral triangles, right triangles, angles, lines, . . . (This is not meant to suggest that students don’t eventually need to know the meanings of “prove” and “similar.”)

There’s a nice animation for rigid motions at http://www.girlsangle.org/page/videos.html. See the Gingerbread Transformer which talks about packing shapes into boxes. If the transformer in the animation got a dilation button, and the shapes and boxes got labels like “triangle” or “equilateral triangle,” one could ask what shapes could be packed into what boxes, e.g., could you take any shape labeled “triangle” and pack it into any box labeled “triangle.”

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