Yes.
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A square, rectangle, rhombus, parallelogram, trapezium, kite and arrowhead will tessellate. Other quadrilaterals will not.
A trapezium. A trapezium. A trapezium. A trapezium.
Yes a quadrilateral will tessellate.
No, but an octagon and a square can tessellate.
There is no general relationship.All triangles will tessellate. All quadrilaterals will tessellate There are 15 classes of convex pentagons (the latest discovered in 2015) which will tessellate. Regular hexagons will tessellate. In addition, there are 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.