A single shape, repeated by sliding (and sometimes rotating or flipping) it, can cover the whole plane with no gaps or overlaps. Here is one shape per tile: the familiar quadrilaterals and triangles, some deliberately irregular ones, plus a pentagon and a regular hexagon.
Useful facts on show: every triangle tiles the plane, and so does every quadrilateral — even an irregular or non-convex one — because two copies (one turned 180°) always fit together into a shape that repeats. Most shapes here are intentionally irregular (unequal sides and angles) so you can see the tiling does not need a "nice" shape.
Every tiling shown was verified to cover the plane with no gaps or overlaps. Triangles and quadrilaterals are tiled using two copies (the second rotated 180°); parallelograms, rhombi, the pentagon and the hexagon repeat directly. The two general-convex-quadrilateral cards show two different tilings of the same shape, made by turning the copy about a different edge.