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Yes. A simple case would be where they combine into a square.
Yes. A regular tessellation can be created from either an equilateral triangle, a square, or a hexagon.
A chessboard is tessellated, so I assume it is a figure that is checkered.
A square is one of the simplest shapes that can be tessellated. Tessellation is the means of using a repeated shape to build a larger shape with no gaps or overlaps.
Yes