Proof of Proposition 28, Book XI, Euclid's Elements
This Demonstration shows a proof by dissection of Proposition 28, Book XI of Euclid's Elements: if a parallelepiped is cut by a plane through the diagonals of the opposite planes, then the solid is bisected by the plane.
The blue and the orange prisms are only symmetrical; to prove that they are equivalent, certain propositions are needed .
 D. E. Joyce, "Euclid's Elements: Introduction."  Euclid, Elements, T. L. Heath, trans., as The Thirteen Books of Euclid’s Elements, 2nd ed., Book 3, New York: Dover Publications, 1956 pp. 332–333.