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recommended investigations


Tessellation Restrictions: Determine which polygons can tessellate.

Vertex Angles in a Regular Polygon: Investigate how the vertex angle of a regular polygon relates to its number of sides.

Sum of Angles in a Polygon: Explore the relationship between the number of sides of a polygon and the sum of its interior angles.

Sum of Exterior Angles: Determine the sum of the exterior angles in any polygon.

Constructing a Square: Use a dynamic software tool to construct a square in different ways.

Medial Polygons: Investigate the characteristics of a polygon that is generated by connecting the midpoints of consecutive sides of a polygon.

Triangles in Hexagons: Determine the probability that a point inside a hexagon is also inside a triangle that shares common vertices.

Pentagons with Restricted Perimeter: Find the largest possible area of a pentagon with a restricted perimeter.

Apothem and Area: Explore the relationship between the apothem, perimeter, and area of a regular polygon.

Divide into n-th segment: Divide sides of a polygon to construct polygons in the interior region of another polygon.


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