In the geometry shown in the figure, the quadrilateral ABCD is a square, Ma ⊥ plane ABCD, PD ∥ Ma, e, G, f are the midpoint of MB, Pb, PC respectively, and ad = PD = 2mA. (I) verification: plane EFG ⊥ plane PDC; (II) calculation of the volume ratio of triangular pyramid p-mab and quadrangular pyramid p-abcd

In the geometry shown in the figure, the quadrilateral ABCD is a square, Ma ⊥ plane ABCD, PD ∥ Ma, e, G, f are the midpoint of MB, Pb, PC respectively, and ad = PD = 2mA. (I) verification: plane EFG ⊥ plane PDC; (II) calculation of the volume ratio of triangular pyramid p-mab and quadrangular pyramid p-abcd

(1) It is proved that: from the known Ma ⊥ plane ABCD, PD ∥ Ma, so PD ⊥ plane ABCD and BC ⊂ plane ABCD, because the quadrilateral ABCD is square, so PD ⊥ BC and PD ∩ DC = D, so BC ⊥ plane PDC is in △ PBC, because g and F are the midpoint of Pb and PC respectively, so GF ⊉ BC, so GF ⊥ plane PDC and GF ⊂ plane EFG, so plane EFG ⊥ plane PDC; (II) because PD ⊥ plane ABCD, four If the edge shape ABCD is a square, let Ma = 1, then PD = ad = 2, so vp-abcd = 13s square ABCD, PD = 83. Because of the distance between Da ⊥ plane mAb, Da is the distance from point P to plane mAb, and the triangular pyramid VP mAb = 13 × 12 × 1 × 2 × 2 = 23, so vp-mab: vp-abcd = 1:4