a rhombus
/ ROM-bus /
A rhombus is the shape on a playing card's diamond suit, or a squashed square — a four-sided figure with all four sides the same length but corners that lean rather than stand square. A garden lattice of equal diagonal slats, or the diamond markings on a road, trace out rhombi.
Precisely, a rhombus is a parallelogram with all four sides equal. Because it is a parallelogram first, it inherits everything a parallelogram has — opposite sides parallel, opposite angles equal, diagonals bisecting each other — and then its equal sides force two extra special properties: its diagonals are perpendicular to each other, and each diagonal bisects the pair of angles it passes through. So the two diagonals of a rhombus meet at right angles, cutting the figure into four congruent right triangles. A rhombus need not have right angles at its corners; only when it does is it a square.
The rhombus is the 'equal-sides' branch of the parallelogram family, sitting opposite the rectangle (the 'equal-angles' branch); the square is exactly the overlap, the polygon that is both. A useful test runs backwards: a parallelogram whose diagonals are perpendicular is a rhombus, and so is one in which a diagonal bisects a vertex angle. The misconception to avoid is calling any four-equal-sided figure a 'square' — equal sides give a rhombus, but you also need right angles (or equal diagonals) to upgrade it to a square.
A rhombus with side 5 and diagonals 6 and 8: the diagonals cross at right angles and bisect each other, so they split the rhombus into four right triangles with legs 3 and 4 — and indeed 3^2 + 4^2 = 5^2, matching the side length.
Perpendicular, mutually bisecting diagonals split a rhombus into four right triangles.
A rhombus has equal sides but not necessarily right angles; equal sides alone do not make a square. Add right angles (equivalently, equal diagonals) and the rhombus becomes a square.