Proof: if the projection from the vertex of a triangular pyramid to the bottom is the perpendicular center of the bottom triangle, then the projection from any vertex of the bottom triangle to the opposite side must also be the perpendicular center of the triangle

Proof: if the projection from the vertex of a triangular pyramid to the bottom is the perpendicular center of the bottom triangle, then the projection from any vertex of the bottom triangle to the opposite side must also be the perpendicular center of the triangle

It is known that: as shown in the figure, in the triangular pyramid p-abc, Po ⊥ plane ABC, O is the vertical center of △ ABC. Prove: the projection of a in the plane PBC is the vertical center of △ PBC. Prove: connect Ao to D, ⊥ Po ⊥ plane ABC, BC ⊂ plane ABC, ⊥ Po ⊥ BC ⊥ o is the vertical center of △ ABC, ⊥ BC ⊥ Ao ∩ Po ∩ Ao = O, ∩ BC ⊥ plane pad, so BC ⊥ PA, ab ⊥ PC. because of BC ⊥ plane pad, it is flat If we make ah ⊥ PD in H, then ah ⊥ plane PBC, so BH is the projection of AB in plane PBC. Because ab ⊥ PC, from the three perpendicular theorem, BH ⊥ PC. and BC ⊥ PD, ⊥ h is the perpendicular center of △ PBC