Question

Only three regular polygons can tessellate in a plane.

Define tessellation
Name the three regular polygons
Explain why a regular polygon cannot form a tessellation.
Explain why only these three can form a tessellation.

Answer 1

Repeaterd use of figures of one kind or more to cover a plane without gaps and without overlaps is called tessellation.
only equilateral triangles squares and regular hexagons can form tessellation.
it is because each of their interior angles should be a factor of 360°. only these 3 kinds satisfy this.

Answer 2

Answer:

1. Define tessellation.

Tessellation is an arrangement of polygons in a repeated pattern without gaps or overlapping.

2. Name the three regular polygons.

Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.

3. Explain why a regular polygon cannot form a tessellation.

The interior angle of a polygon should divide 360 degrees evenly, so as to tessellate. The polygons whose internal angles do not divide 360 degrees do not tessellate. Like octagon is 135° which does not divide into 360°.

4. Explain why only these three can form a tessellation.

The triangles have an interior angle of 60 degrees that can divide 360 degrees. The square has interior angle of 90 degrees that divides 360 degrees.