In a triangular pyramid a-bcd, the projection of D in plane ABC is e, and the projection of a in plane BCD is f (1) If de intersects AF, verify that ad is perpendicular to BC (2) Is the inverse proposition of (1) Tenable

In a triangular pyramid a-bcd, the projection of D in plane ABC is e, and the projection of a in plane BCD is f (1) If de intersects AF, verify that ad is perpendicular to BC (2) Is the inverse proposition of (1) Tenable

(1) F is the projection of a in plane BCD = > AF ⊥ plane BCD = > AF ⊥ BCE is the projection of D in plane ABC = > de ⊥ plane ABC = > de ⊥ BC, and de intersects AF = > A, D, e, f are coplanar (set as plane α), then BC ⊥ plane α, then BC ⊥ ad (2) by the inverse theorem of three perpendicular theorem, ad ⊥ BC, then DF ⊥ BC, then BC