* Scissors congruence:
A sc= B means figure A can be cut into pieces that can be reassembled to
form figure B.
This is also described
using the word "equidecomposable". "A and B are equdecomposable to
SC = is a reflexive, symmetric, and transitive
relation. [like congruence and similarity in geometry and equality in arithmetic]
Theorem I : A sc= B implies Area(A) = Area(B)
Theorem II [The converse of Theoerm
I!]: Area(A) = Area(B) implies A sc= B !!
Simple cases as evidence and a foundation for building toward
the proof of Theorem II.: