Angle C of triangle ABC is straight line. AD – perpendicular to the plane Δ ABC. Prove that Δ BCD is rectangular.

Three perpendicular theorem: 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 inclined one.

BC – a straight line drawn on the plane ABC through the base of the inclined (through point C).

AC – projection of oblique DC.

AC is perpendicular to BC, because angle C = 90 degrees. Hence, according to the three perpendicular theorem, DC is perpendicular to BC. Whence it follows that the angle BCD is right and Δ BCD is rectangular.