NamingĪ tessellation of squares is named by choosing a vertex and then counting the number of sides of each shape touching the vertex. The parallelogram is then translated on the diagonal and to the right and to the left. These tessellations work because all the properties of a tessellation are present.įigure 10.97 Tessellating with Obtuse Irregular Trianglesįirst, the triangle is reflected over the tip at point A A, and then translated to the right and joined with the original triangle to form a parallelogram. Both tessellations will fill the plane, there are no gaps, the sum of the interior angle meeting at the vertex is 360 ∘, 360 ∘, and both are achieved by translation transformations. The interior angle of a hexagon is 120 ∘, 120 ∘, and the sum of three interior angles is 360 ∘. ![]() There are three hexagons meeting at each vertex. In Figure 10.79, the tessellation is made up of regular hexagons. An interior angle of a square is 90 ∘ 90 ∘ and the sum of four interior angles is 360 ∘. There are four squares meeting at a vertex. In Figure 10.78, the tessellation is made up of squares. For a tessellation of regular congruent polygons, the sum of the measures of the interior angles that meet at a vertex equals 360 ∘.In other words, if you were to draw a circle around a vertex, it would include a corner of each shape touching at that vertex. ![]()
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