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 Splitting shapes (Posted on 2006-02-16)
1. Divide a square into three similar regions, ALL THREE of which are congruent.
2. Divide a square into three similar regions, EXACTLY TWO of which are congruent.
3. Divide a square into three similar regions, NO TWO of which are congruent.
4. Divide an equilateral triangle into three similar regions, ALL THREE of which are congruent.
5. Divide an equilateral triangle into three similar regions, EXACTLY TWO of which are congruent.
6. Divide an equilateral triangle into three similar regions, NO TWO of which are congruent.

If necessary, you may use one or more inversely similary regions where all corresponding angles are equal and described in the opposite rotational sense, i.e. "reflected".

 See The Solution Submitted by Bob Smith Rating: 4.0000 (3 votes)

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 Pictures of solutions | Comment 2 of 9 |

http://www.mohawk.mtrsd.k12.ma.us:8000/site/dept/math/jgalvagni/splitting_shapes.gif

There are multiple solutions to some of these:

2.  Can also be done by drawing a diagonal and then bisecting one of the resulting isosceles right triangles.

4.  Can be done with any 3 lines or curves radiating from the center 120 degrees apart.

 Posted by Jer on 2006-02-16 13:19:09

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