In the triangular pyramid p-abc, point O is perpendicular to the triangle ABC, and Po is perpendicular to the plane ABC

In the triangular pyramid p-abc, point O is perpendicular to the triangle ABC, and Po is perpendicular to the plane ABC

Connect O and a B C BC ⊥ Ao, Ao is the projection of AP on the bottom, so BC ⊥ AP is the same as others

From a point in the dihedral angle to two half planes, it is proved that their angles complement the plane angles of the dihedral angle

It is proved that: let a point P in the dihedral angle m-a-n, PA ⊥ plane m at point a, PD ⊥ plane n at point D, make DC ⊥ a at point C, make ab ⊥ plane n, ∵ ab ∥ PD, point P, a, B, C and D are in the same plane, ∵ point D is on BC, ∵ ab ⊥ plane n, DC ⊥ a, ∵ AC ⊥ a, ∵ ACD are the plane angles of dihedral angle m-a-n, ∵ quadrilateral APDC, ∵ PDC = ∠ PAC = RT ∠, ∩ APD + ∧ ACD = 180 ° that is from the plane angle A point in a dihedral angle is perpendicular to two half planes, and their angles are complementary to the plane angles of the dihedral angle