The Cross Section of a Tetrahedron. Model 4

Let's consider the most general case in which all the three given points K, L, and M lie on the pyramid's faces.

  1. As in the previous case, we draw the auxiliary plane CKM, which meets the edges SA and SB at E and F respectively.
  2. Draw KM, the trace of the section plane on the plane CKM, and mark the intersection point P of KM and EF.
  3. Point P, as well as L, lies in the plane SAB, so the line PL is the trace of the section on the plane SAB and its intersection points with SA and SB are the vertices of the section.
  4. Now we can construct the traces of the section on the planes SAC and SBC and mark their intersection points with the edges AC and BC.
  5. All the four vertices of the section have been constructed; it remains to join them.