The Cross Section of a Tetrahedron. Model 7

Points K, L and M are given on three faces of a pyramid. Let's draw the section through these points without going out of the pyramid. Suppose that the section have already been constructed.

ANALYSIS: CONSTRUCTION:

Suppose that the section plane cuts the edge CB at point P. Denote by F the intersection point of KM and LP. Construct the central projections of the points K, F and M from the center C onto the plane SAB and denote them by K1, F1 and M1. The points K1 and M1 can be found easily, and the point F1 is on the intersection of K1M1 and LB.

  1. Construct the central projections of the points K and M from the center C onto the plane SAB and denote them by K1 and M1.
  2. Draw the lines K1M1 and LB and mark their intersection point; denote it by F1.
  3. Draw the lines CF1 and KM and mark their intersection point; denote it by F.
  4. Draw the line LF and mark point P, its intersection point with the edge CB. This is the first vertex of the section.
  5. Draw the line PM and mark its intersection point with the edge SB. This is the second vertex of the section.
  6. From the second vertex, draw the line through L and find the third vertex of the section.
  7. From the third vertex, draw the line through K and find the fourth vertex of the section.
  8. All the four vertices of the section have been constructed; it remains to join them.