Name three regular polygons that will tessellate the plane
triangle, quadrilateral, and hexagon
To identify regular polygons that can tessellate the plane, we need to find polygons with angles that divide evenly into 360 degrees. Here are three regular polygons that tessellate the plane:
1. Equilateral Triangle: An equilateral triangle has three equal sides and three equal angles measuring 60 degrees each. Since 60 degrees divides evenly into 360 degrees (360 ÷ 60 = 6), we can create a tessellation with equilateral triangles.
2. Square: A square has four equal sides and four right angles measuring 90 degrees each. Since 90 degrees divides evenly into 360 degrees (360 ÷ 90 = 4), we can use squares to create a tessellation.
3. Hexagon: A regular hexagon has six equal sides and six angles measuring 120 degrees each. Since 120 degrees divides evenly into 360 degrees (360 ÷ 120 = 3), we can create a tessellation with regular hexagons.
To tessellate the plane, arrange these regular polygons without any gaps or overlaps, covering the entire plane using repetitions of the same shape.