In any parallelogram the parallelograms about the diagonal are similar to the whole, and to one another. * Let $ABCD$ be a parallelogram, and $AC$ its diagonal. * And let $EG$ and $HK$ be parallelograms about $AC$. * I say that the parallelograms $EG$ and $HK$ are each similar to the whole (parallelogram) $ABCD$, and to one another.
If a parallelogram is divided into four parallelograms, then the two parallelograms lying on the diagonal are similar to each other and to the whole parallelogram.
Proofs: 1