In the triangle ABC, the angle is C = 90, AD is perpendicular to the plane (ABC). Prove that the triangle DBC is right-angled.

Since the segment AD is perpendicular to the plane of the triangle ABC, it is perpendicular to the AC side of the triangle. Angle CAD = 90.

CD is inclined to the plane ABC, then AC is the projection on the plane.

By condition, AC is perpendicular to CB, angle ACB = 90.

The straight line BC lies on the plane ABC and is perpendicular to the projection of the inclined CD, then the inclined line itself is perpendicular to the segment BC. The angle ВСD = 90, which means that the triangle DBС is rectangular, which was required to be proved.