Answer:<em> If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. To prove a square, you must prove it is both a rectangle and a rhombus.</em>
For the most part, the cross-section formed is a <em>trapezoid</em>, but if the slice passes through the apex of the pyramid, that shape is a <em>triangle</em>.