The sign of perpendicular planes

Theorem

If a plane passes through a straight line perpendicular to another plane, then these planes are perpendicular.



Evidence

Let α be the plane, b the straight line perpendicular to it, β the plane passing through the straight line b, and c the straight line along which the planes α and β intersect. Prove that α and β are perpendicular.
Draw in the plane α through the intersection point of line b with plane α a line a, perpendicular to line c. Draw through the lines a and b the plane γ. It is perpendicular to line c, since line c is perpendicular to lines a and b. Since the lines a and b are perpendicular, the planes α and β are perpendicular. The theorem is proved.