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YES! They CAN tessellate! Triangles, squares, and hexagons are the only shapes that can tessellate by themselves!
So yes, squares can tesselate!
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Yes.
Yes, it will.
True * * * * * No. The only regular polygons that will tessellate are a triangle, a square and a heagon. So a regular heptagon will not tessellate.
An equilateral triangle, a square and a hexagon.
square, equillateral triangle, & regular hexagon