What about a hexagon where each pair of opposite sides is parallel, and opposite sides are the same length, but different pairs of sides are not the same length?
Do all hexagons of this form tessellate? How do you know?
Now let's consider hexagons with three adjacent angles which add up to $360^{\circ}$, sandwiched by two sides of equal length, as in the diagram below:
Is it true that any hexagon of this form will tessellate? How do you know? Click below for a hint that might help you get started.
You could start by convincing yourself that sides $y$ and $z$ are parallel...
Can you find a hexagon which doesn't have a pair of equal parallel sides, but still tessellates?