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".

(In reply to re(2): All but 5 by Dej Mar)

I assure you the rectangles for 3 and the pentagons for 5 are similar in the geometric sense.  The proportions are given in the pictures.

Posted by Jer on 2006-03-16 13:12:10