Honors Geometry Companion Book, Volume 2

12.2.2 Tessellations (continued)

It is determined in this example whether a regular polygon can be used to form a tessellation and why. Physically, the figures do tessellate. The angles of the equilateral triangles are 60°, and the angles of the square are 90°. The only way to combine both of these values to produce 360° is with three 60° angles and two 90° angles, or three triangles and two squares. These are the figures that come into contact at each vertex of the tessellation.

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