No convex polygon with 7 or more sides will tessellate.
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True
Mostly true - you cannot tessellate only regular pentagons in two dimensions, since you cannot sum up the intersection of the angles to 360 degrees. If you tessellate a regular pentagon in three dimensions, you end up with a dodecahedron.
Yes, it is true.
Not necessarily. If the statement is "All rectangles are polygons", the converse is "All polygons are rectangles." This converse is not true.
No, it is not true that you cannot tessellate a six-sided polygon by itself. Hexagons are a type of polygon that can tessellate, which means they can be arranged in a repeating pattern to completely cover a plane without any gaps or overlaps.