![]() 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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