Question 23
(BUL) Three faces of a tetrahedron are right triangles, while the fourth is not an obtuse triangle.
(a) Prove that a necessary and sufficient condition for the fourth face to be a right triangle is that at some vertex exactly two angles are right.
(b) Prove that if all the faces are right triangles, then the volume of the tetrahedron equals one-sixth the product of the three smallest edges not belonging to the same face.
(a) Prove that a necessary and sufficient condition for the fourth face to be a right triangle is that at some vertex exactly two angles are right.
(b) Prove that if all the faces are right triangles, then the volume of the tetrahedron equals one-sixth the product of the three smallest edges not belonging to the same face.