Which regular polygon can be used to form a tessellation?
https://www.mathsisfun.com/geometry/tessellation.html
To determine which regular polygon can be used to form a tessellation, we need to understand what a tessellation is. A tessellation is a pattern of shapes that completely covers a plane without any gaps or overlaps.
For a regular polygon to create a tessellation, it must satisfy a specific condition called the "vertex angle sum theorem." According to this theorem, the angle measure at each vertex of the polygon must evenly divide 360 degrees.
Let's consider the following regular polygons:
1. Triangle (Equilateral): Each interior angle of an equilateral triangle measures 60 degrees. Since 360 divided by 60 is 6, it is possible to tessellate the plane with equilateral triangles.
2. Quadrilateral (Square): Each interior angle of a square measures 90 degrees. Since 360 divided by 90 is 4, it is possible to tessellate the plane with squares.
3. Pentagon: Each interior angle of a regular pentagon measures 108 degrees. Since 360 divided by 108 is not a whole number, a regular pentagon cannot tessellate the plane without gaps or overlaps.
4. Hexagon: Each interior angle of a regular hexagon measures 120 degrees. Since 360 divided by 120 is 3, it is possible to tessellate the plane with regular hexagons.
Finally, we can conclude that the regular polygons that can be used to create tessellations are the equilateral triangle and the square.