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Name: 
qquad
14
m Concietrion
G.1
A regular polygon is a shape that has equal sides and equal angles. There are only 3 regular polygons that can form tessellations by themselves. Other regular polygons can be used together to form a tessellation.
Part 1
Will the regular polygon tessellate?
Part 2
Describe the 3 regular polygons that will tessellate




Regular Polygon
Number of Sides


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2)



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Name: \qquad \newline1414\newlinem Concietrion\newlineG.11\newlineA regular polygon is a shape that has equal sides and equal angles. There are only 33 regular polygons that can form tessellations by themselves. Other regular polygons can be used together to form a tessellation.\newlinePart 11\newlineWill the regular polygon tessellate?\newlinePart 22\newlineDescribe the 33 regular polygons that will tessellate\newline\begin{tabular}{|l|l|}\newline\hline \multicolumn{11}{|c|}{ Regular Polygon } & Number of Sides \\\newline\hline 11) & \\\newline\hline 22) & \\\newline\hline 33) & \\\newline\hline\newline\end{tabular}

Full solution

Q. Name: \qquad \newline1414\newlinem Concietrion\newlineG.11\newlineA regular polygon is a shape that has equal sides and equal angles. There are only 33 regular polygons that can form tessellations by themselves. Other regular polygons can be used together to form a tessellation.\newlinePart 11\newlineWill the regular polygon tessellate?\newlinePart 22\newlineDescribe the 33 regular polygons that will tessellate\newline\begin{tabular}{|l|l|}\newline\hline \multicolumn{11}{|c|}{ Regular Polygon } & Number of Sides \\\newline\hline 11) & \\\newline\hline 22) & \\\newline\hline 33) & \\\newline\hline\newline\end{tabular}
  1. Check Interior Angles: To determine if a regular polygon will tessellate, we need to check if the interior angles can fit together at a point without any gaps or overlaps. The formula for the interior angle of a regular polygon is (n2)×180/n(n-2) \times 180^\circ / n, where nn is the number of sides.
  2. Tessellation Criteria: Part 11: A regular polygon will tessellate if the interior angle divides evenly into 360°360°. This is because the angles at each vertex of the tessellation must add up to 360°360°.
  3. Regular Polygons: Part 22: The three regular polygons that can tessellate by themselves are the equilateral triangle, the square, and the regular hexagon. We can check this by calculating their interior angles and seeing if they divide evenly into 360360^\circ.
  4. Equilateral Triangle: For the equilateral triangle (33 sides): The interior angle is (32)×180°/3=60°(3-2) \times 180° / 3 = 60°. Since 360°/60°=6360° / 60° = 6, which is a whole number, equilateral triangles tessellate.
  5. Square: For the square (44 sides): The interior angle is (42)×180/4=90(4-2) \times 180^\circ / 4 = 90^\circ. Since 360/90=4360^\circ / 90^\circ = 4, which is a whole number, squares tessellate.
  6. Regular Hexagon: For the regular hexagon (66 sides): The interior angle is (62)×180°/6=120°(6-2) \times 180° / 6 = 120°. Since 360°/120°=3360° / 120° = 3, which is a whole number, regular hexagons tessellate.
  7. List of Tessellating Polygons: Now, let's list the regular polygons that tessellate:\newline11) Equilateral Triangle (33 sides)\newline22) Square (44 sides)\newline33) Regular Hexagon (66 sides)

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