ABCD-rectangle, M does not lie (ABC), angle MBC = 90. Prove AD is perpendicular to AM.

MV⊥VS, AV⊥VS. ⇒ the base H of the perpendicular from M to the plane ABC belongs to AB, because HB is the projection of the MV onto the plane of the rectangle.

VN – projection of MV on the plane ABC, AN – projection of MA on the plane ABC. BA⊥AD. By so about 3 perpendiculars: If a straight line drawn on a plane through the base of an inclined one is perpendicular to its projection, then it is perpendicular to the most inclined one. ⇒
AD is perpendicular to AM.