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GeoGebraGeoGebra Classroom

Cross Sections of the Regular Tetrahedron

Given is a regular tetrahedron ABCD. Let P be a point on BD, Q a point on AD, and R a point on CD or AC.
  • Drag the points P,Q and R and explore the shape of the cross section of the blue plane and the tetrahedron.
  • Use different combinations of the checkboxes to explore some special cases.
  • In what position of the points the section is a trapezoid, or a rectangle, or a square, or a triangle, or an isosceles triangle, or an equilateral triangle?
  • In each case justify your conjecture.