91Ó°ÊÓ

Show that the locus of points within a dihedral angle and equidistant from its faces is the plane bisecting the dihedral angle.

Prove that a plane is determined by a line and a point not on that line. Also show that the plane contains the given line.

Prove that there exists a plane \(\mathrm{M}\) which is perpendicular to a line \(L\) at a point \(P\) on \(L\).

Show that if a line is perpendicular to one of two parallel planes, then it is perpendicular to the other.

Show that parallel planes are everywhere equidistant.

Given that \(\underline{\mathrm{AB}}\) is perpendicular to plane \(\mathrm{P}, \underline{\mathrm{BC}}\) and \(\underline{\mathrm{BD}}\) lie in plane \(\mathrm{P}\), and \(\underline{\mathrm{BC}} \cong \underline{\mathrm{BD}}\), prove that \(\underline{\mathrm{AC}} \cong \mathrm{AD}\).

If two planes are perpendicular to each other, prove that a line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.

\(\mathrm{ABCD}\) is a rectangle. \(\underline{\mathrm{PA}}\) is perpendicular to the plane of the rectangle and the line \(\underline{P B}\) is drawn. Prove that \(\angle P B C\) is a right angle.

Line \(\mathrm{k}\) is parallel to plane \(\mathrm{P}\). Prove that a plane perpendicular to line \(\mathrm{k}\) is also perpendicular to \(\mathrm{P}\).

Show that two lines perpendicular to the same plane are parallel.