Construct a plane that contains a point near a vertex (other than vertex A) on one of the three edges, a point in the middle of another one of the edges, and a third point that is neither in the middle nor coinciding with the first point. Pick a vertex, let’s say A, and consider the three edges meeting at the vertex. One way to obtain a rectangle that is not a square is by cutting the cube with a plane perpendicular to one of its faces (but not perpendicular to the edges of that face), and parallel to the four, in this case, vertical edges.
Problem C1Ī square cross section can be created by slicing the cube by a plane parallel to one of its sides.Īn equilateral triangle cross section can be obtained by cutting the cube by a plane defined by the midpoints of the three edges emanating from any one vertex.
What cross sections can you get from each of these figures?Ĭross Sections adapted from Connected Geometry, developed by Educational Development Center, Inc. Explain what makes them impossible.įind a way to slice a tetrahedron to make a square cross section. The Interactive Activity provides you with one way to make each of the shapes that you can, in fact, make as a cross section.Ī couple of the shapes on the list in Problem C1 are impossible to make by slicing a cube. Record which of the shapes you were able to create and how you did it. Try to make the following cross sections by slicing a cube: a. How may faces does a cube have? Each side of your cross section comes from cutting through a face of your cube.