Solids > Cross sections

Here you see a cross-section $APGQ$ drawn inside a cube. $P$ and $Q$ are the centers of the edges on which they are situated.

A cross-section of a 3D figure with a plane is the figure composed of all secants (intersecting lines). If this cross-section is a triangle you can be sure that is indeed a plane. With quadrangles, pentagons, et cetera you should look more carefully to verify that such a figure eally is a plane, you can use the fact that only two parallel or intersecting lines can form a plane.

When drawing a cross-section, you use the fact that the secants of a plane with two parallel planes are themselves parallel.

To be able to do calculations in cross-sections you need to draw them life sized. By this we mean that all angles have its real shape and that all sides their real length (drawn to a scale if necessary). When drawing life sized figures you often construct triangles using a pair of compasses. As an aid you draw figures of which you already know the dimensions to find unknown lengths and angles.