Will All Quadrilaterals Tessellate?

All quadrilaterals tessellate. Begin with an arbitrary quadrilateral ABCD. Rotate by 180° about the midpoint of one of its sides, and then repeat using the midpoints of other sides to build up a tessellation. The angles around each vertex are exactly the four angles of the original quadrilateral.

Can irregular quadrilaterals tessellate?

A year 8 teacher wrote on the board, "Any quadrilateral will tessellate". ... The diagram below shows an irregular quadrilateral which has been flipped and rotated to cover the space around a point. This group of four identical quadrilaterals can be then be replicated to cover the whole surface.

Can congruent quadrilaterals tessellate?

A shape is said to tessellate the plane if the plane can be covered without holes and no overlapping (save for the boundary points) with congruent copies of the shape. Squares, rectangles, parallelograms, trapezoids tessellate the plane; each in many ways. ... Any triangle therefore also tessellates the plane.