Will any kite tessellate the plane? why or why not?
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To determine whether any kite can tessellate the plane, we need to consider the properties of a kite and the requirements for tessellation.
A kite is a quadrilateral with two pairs of adjacent sides of equal length. It has an axis of symmetry that bisects the angles opposite each other. However, not all kites can tessellate the plane.
Tessellation refers to the arrangement of shapes to completely cover a surface without any gaps or overlaps. In order to form a tessellation, the shape must meet two conditions:
1. The interior angles of the shape must add up to a multiple of 360 degrees.
2. The sides of the shape must fit together without leaving any gaps.
If we consider all possible kites, we can observe that a regular kite (i.e., a kite with all sides and angles equal) will not tessellate the plane. This is because the interior angles of a regular kite are 90 degrees, 90 degrees, 90 degrees, and 90 degrees, which totals 360 degrees. However, the sides of a regular kite will not fit together without gaps.
On the other hand, if we allow irregular kites (kites with sides and/or angles of different lengths), it is possible to find specific irregular kites that can tessellate the plane. For example, specific combinations of different irregular kites can fit together to create a tessellation.
In conclusion, while regular kites cannot tessellate the plane, specific combinations of irregular kites may be able to form a tessellation.