A triangle is rigid and a square is not
Why triangulation is the whole basis of framed structures.
A triangle is rigid because its three sides fix its three angles completely, so the only way to change its shape is to change the actual length of a side, while a square or any other shape with more than three sides can rack into a different shape entirely, with every side keeping its own length exactly the same.
Gordon's Structures: Or Why Things Don't Fall Down is older than I am, and it was the first book that made me see a chassis not as a collection of tubes but as a set of decisions about which shape each panel of it was allowed to become.
Three lengths fix three angles
Three rigid rods pinned together at their ends can only ever form one triangle, because once the length of each side is fixed, the angles between them are fixed along with it, a fact that follows purely from the geometry, whatever the rods are made of. Four rigid rods pinned together at their corners to form a square or a rectangle have no such guarantee, since the same four side lengths can also form a leaning parallelogram, or something flatter still, all with every side exactly the length it started at. Strong rods do nothing to prevent this racking, because the rods never bend or break; the whole shape simply swings sideways at its pinned corners while every side stays perfectly rigid. Add a diagonal rod across two opposite corners of that same four-sided shape, though, and the whole thing is instantly locked, because that single diagonal has split the shape into two triangles, and a triangle, as already established, cannot rack. The rule holds for any number of sides. A pentagon needs two internal diagonals and a hexagon three to split it into triangles, and once split it is locked just as completely as a braced square.
A sagging garden gate
A folding clothes-drying rack or an old wooden garden gate shows this exact failure over years of ordinary use. Built as a simple rectangular frame with no bracing, it gradually leans and racks sideways into a slanted parallelogram shape, the joints at each corner having loosened just enough to let the whole rectangle swing over time even though every individual rail is still perfectly straight and undamaged. The fix, adding a single diagonal strut running from one corner to the opposite one, stops the racking instantly and completely by turning the loose four-sided shape into two triangles that geometry itself will not allow to change shape. The rails that were racking have not been made any stronger at all. A second diagonal running the other way across the same rectangle adds nothing further once the first one is in place, since the shape is already fully locked, so bracing the same panel twice buys no extra resistance to racking.
A braced frame can still snap
Triangulation explains why a framed structure resists changing its overall shape, but it says nothing on its own about how much load any individual member of that structure can actually carry before it bends or snaps, which is a separate question about the strength and stiffness of the material each rod is made from. A structure can be triangulated perfectly and still fail, if the individual rods are too thin or too weak for the loads passing through them, exactly as a triangle built from drinking straws holds its shape under a gentle push but still buckles once pushed hard enough. Triangulation fixes the shape and leaves the strength of each member as a separate job, and a real structure needs both handled, much as a locked door still needs a frame strong enough to carry the door's weight however well the lock works.
Reading a chassis drawing for its triangles
This is why a tubular chassis, a roll cage, or almost any lightweight framed structure is built almost entirely from triangles, since every panel that is left untriangulated is a panel relying purely on the stiffness of its joints to hold its shape, and joints are almost always the weakest, most flexible part of any welded or bolted structure. A designer looking at a chassis drawing can read its structural soundness directly from its shape alone, checking whether every open panel has been split by a diagonal member, because any panel that has not been is a panel that will rack under load regardless of how thick or strong the tubes forming its sides happen to be. Where a panel has to stay open, for a door or for a driver to climb in, the designer either makes its corner joints far stiffer than usual or triangulates the panels around it more heavily to carry the load past the gap. This habit of reading a drawing for its triangles, before looking at any material thickness or joint specification at all, is one of the fastest ways an experienced eye can spot a weak panel on a chassis long before it is ever built and tested.