We call a tetrahedron right-faced if each of its faces is a right-angled triangle.(a) Prove that every orthogonal parallelepiped can be partitioned into six right-faced tetrahedra.(b) Prove that a tetrahedron with vertices A1,A2,A3,A4 is right-faced if and only if there exist four distinct real numbers c1,c2,c3, and c4 such that the edges AjAk have lengths AjAk=∣cj−ck∣ for 1≤j<k≤4. geometry3D geometrytetrahedrongeometry unsolved