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What kinds of regular polygons can be used for regular tessellations?Check all that apply.A.Six-sidedB.Eight-sidedC.Five-sidedD.Three-sided

Question

What kinds of regular polygons can be used for regular tessellations?Check all that apply.A.Six-sidedB.Eight-sidedC.Five-sidedD.Three-sided

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Solution

A regular tessellation is a pattern made by repeating a regular polygon.

A. Six-sided: Yes, a regular hexagon (six-sided polygon) can be used for regular tessellations. Six equilateral triangles meet at each vertex, so it tessellates.

B. Eight-sided: No, a regular octagon (eight-sided polygon) cannot be used for regular tessellations. The interior angle of an octagon is 135 degrees, which does not divide evenly into 360.

C. Five-sided: No, a regular pentagon (five-sided polygon) cannot be used for regular tessellations. The interior angle of a pentagon is 108 degrees, which does not divide evenly into 360.

D. Three-sided: Yes, a regular triangle (three-sided polygon) can be used for regular tessellations. Six equilateral triangles meet at each vertex, so it tessellates.

So, the regular polygons that can be used for regular tessellations are six-sided and three-sided polygons.

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