In triangle ABC, the angle is 90 degrees. Point D does not lie in the plane ABC, and DC

In triangle ABC, the angle is 90 degrees. Point D does not lie in the plane ABC, and DC is perpendicular to AC. Prove that line AC is perpendicular to the DCB plane.

Since, by condition, the triangle ABC is rectangular, the segments AC and BC are perpendicular.

Also, the segment CD, according to the condition, is perpendicular to the AC.

Segments CD and CB intersect and lie in the plane DCB.

On the basis of the perpendicularity of a straight line and a plane, if a straight line is perpendicular to two intersecting straight lines belonging to the same plane, then this straight line is also perpendicular to the plane, then the line AC is perpendicular to the plane DCB, which was required to be proved.