The Renaissance period was not only a new era of Humanism, but also a revival of Platonism in which mathematics was the key for understanding the universe. This belief was manifested by Kepler's model of the solar system and Vincenzo Galilei's twelve-tone equal temperament.

Given: ae ≅ ce ; de ≅ be prove: abcd is a parallelogram. we have that ab || dc. by a similar argument used to prove that △aeb ≅ △ced, we can show that △ ≅ △ceb by. so, ∠cad ≅ ∠ by cpctc. therefore, ad || bc by the converse of the theorem. since both pair of opposite sides are parallel, quadrilateral abcd is a parallelogram.