In the triangular pyramid p-abc, PA ⊥ plane ABC, ab ⊥ AC, D, e and F are the midpoint of PA, Pb and PC respectively, connecting De, DF and ef (1) To prove the parallel plane ABC of plane def (2) If PA = BC = 2, the cosine value of dihedral angle a-ef-d is obtained when the volume of triangular pyramid p-abc reaches the maximum

In the triangular pyramid p-abc, PA ⊥ plane ABC, ab ⊥ AC, D, e and F are the midpoint of PA, Pb and PC respectively, connecting De, DF and ef (1) To prove the parallel plane ABC of plane def (2) If PA = BC = 2, the cosine value of dihedral angle a-ef-d is obtained when the volume of triangular pyramid p-abc reaches the maximum

1. ∩ D and E are the midpoints of edges PA and Pb, respectively ∩ De is the median line of △ PAB, ∩ ab ∩ De is the plane PAB, AB & igrave; plane PAB ∩ de ∩ DF = D, De is contained in plane def, DF is contained in plane def, ∩ plane def ∩ plane ABC2