Part A: Describe the shape of a cross section formed by a cut parallel to the base of a triangular prism. Part B: Describe which cross section of a triangular prism would produce a rectangle. Part C: A diagonal slice from vertex to vertex of a triangular prism would produce which shape?

When you make a cut parallel to the base of a triangular prism, the shape of the cross-section will also be triangular. This is because the parallel cut maintains the same proportions and angles of the triangular base, irrespective of where it is made along the height of the prism. To create a rectangular cross-section of a triangular prism, you need to slice the prism perpendicular to its triangular faces. This cut can be done horizontally or vertically, depending on the orientation of the prism and will yield a rectangle that retains the height of the prism while spanning the width between two parallel edges of the triangular base. Making a diagonal slice from one vertex of a triangular prism to the opposite vertex results in a parallelogram shape. This happens because the cut intersects the triangular faces at an angle, effectively capturing the slant of the prism between the two vertices, while still reflecting the dimensions of the triangular base.