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Cross-Sections of the Cube

Construct the following figures according to the teacher's instruction.
Investigate the possible shapes of the sections of a cube with the figures you constructed. Investigate whether the cube can have the following shapes as cross-sections.
  1. Scalene triangles;
  2. Isosceles triangles;
  3. Equilateral triangles;
  4. Rectangles;
  5. Rhombuses;
  6. Parallelograms;
  7. Trapeziums;
  8. Pentagons;
  9. Regular hexagons.