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".

              /\

             /  \

            /    \

           /      \

          /        \

         / ______   \

        /\      /    \

       /  \/\  /      \

      /______\/________\ 

An attempt to illustrate #5, the equilateral triangle

divided into three similar regions, exactly two which 

are congruent.  The two smaller pentagons are inversely

similar to the larger pentagon.  

Edited on March 19, 2006, 5:42 am

Posted by Dej Mar on 2006-03-17 04:18:50