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Because their interior and exterior angles are the same measurements.

Q: Why does all regular polygons of the same number of sides are similar to each other?

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All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.

Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation. However, for polygons with any number of sides, there are irregular versions that can tessellate.

Certain polygons, yes. Squares, Triangles and Hexagons are all shapes which, in their regular form, can tessellate. Other polygons cannot.

For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.

Square, rhombus, regular octagon, other regular polygons with 4n sides (where n is an integer).

Related questions

-- All regular (equilateral) triangles are similar. -- All squares are similar. -- All pentagons are similar. -- All hexagons are similar. . . . etc. Any regular polygon is similar to all other regular polygons with the same number of sides.

All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.All regular polygons with an even number of sides. Also rectangles.

Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation. However, for polygons with any number of sides, there are irregular versions that can tessellate.

Most regular polygons will not - by themselves. In fact, of the regular polygons, only a triangle, square and hexagon will. No other regular polygon will create a regular tessellation.

Certain polygons, yes. Squares, Triangles and Hexagons are all shapes which, in their regular form, can tessellate. Other polygons cannot.

It will tessellate if its vertices divide into 360 degrees evenly. The only regular polygons that will tessellate are an equilateral triangle, a square and a regular hexagon. There are other, non-regular, polygons that will tessellate.

Any regular polygon with an even number of sides.

For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.For regular polygons, the interior angle must be a factor of 360 degrees.Irregular triangles and quadrilaterals (whose angle sums are factors of 360 degrees) will tessellate. For other polygons, I am not aware of any simple rule.

Square, rhombus, regular octagon, other regular polygons with 4n sides (where n is an integer).

Only if it is a regular tetrahedron, regular octahedron, or regular icosahedron. All other geodesics have isosceles triangle faces, not equilateral triangles.

The only regular polygon with an interior angle of 90 degrees is the square, which has four sides. Other polygons can have an interior angle of 90 degrees, but they would not be regular polygons.

Polygons will be similar if they have the same number of sides AND all of their angles are the same. All of their angles are the same if all but one of their angles are the same because with the same number of sides the angles must add up to the same thing. All squares are similar (4 right angles and sides of equal lenght). All rectangles are similar (4 right angles). We know two triangle are similar if two or mare angles are the same, or if one angle is the same and the two adjacent sides are the same length. Variations of this last proof may apply to some other polygons.