The Cross Section of a Tetrahedron. Model 6

The same idea can be used in a different way. Let's start from the end and analyze the construction above. Suppose that, given points K, L and M we have constructed the cross section KLMN.

ANALYSIS: CONSTRUCTION:

Denote by F the intersection point of the diagonals of the quadrilateral KLMN. Draw the line CF and denote by F1 its intersection point with the face SAB. Clearly, F1 is the common point of the lines KB and MA; this observation allows us to construct it.

  1. Draw the lines KB and MA and mark their intersection point F1.
  2. Draw the lines CF1 and LM and mark their intersection point F.
  3. Draw the line KF and mark point N, its intersection point with the edge CB. This is the missing fourth vertex of the section.
  4. All the four vertices of the section have been constructed; it remains to join them.