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Q: What is the only type of polygon that must be regular if it is equiangular?

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Not all are. Not only is it a concave shape, but the interior angles can vary. For a polygon to be regular, it must be equilateral and equiangular.

A rhombus if i remember my geometry its a rhombus A rhombus is NOT equiangular. A square is the only quadrilateral with equal sides and equal angles. An equilateral triangle is also equiangular. Polygons that are equilateral and equiangular are called regular.

An equilateral polygon is one in which all sides are congruent. The angles may or may not be congruent. The simplest example is an equilateral triangle which must also be equiangular and so is a regular polygon. A rhombus is an equilateral quadrangle. The rhombus, in general, is not regular - only the square (a special type of rhombus) is regular.

In general, a diamond shape is neither a square nor a regular polygon. Only in an extreme form is it a square and therefore a regular polygon.

There are only three regular polygons which can make a regular tessellation?

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Not all are. Not only is it a concave shape, but the interior angles can vary. For a polygon to be regular, it must be equilateral and equiangular.

A regular polygon is any polygon that has sides which are the same length and angles whose measures are equal. An equilateral triangle (also equiangular triangle) is a regular polygon. Other isosceles triangles (equilateral triangles are isosceles, but they are an exception) and scalene triangles are not regular polygons. A side note: Only in a triangle is a polygon regular solely if it is equilateral. (Since an equilateral triangle is equiangular as well). This is NOT always true in other polygons, like quadrilaterals, where it can be equilateral but not necessarily equiangular (a rhombus) or equiangular but not equilateral (a rectangle).

A rhombus if i remember my geometry its a rhombus A rhombus is NOT equiangular. A square is the only quadrilateral with equal sides and equal angles. An equilateral triangle is also equiangular. Polygons that are equilateral and equiangular are called regular.

It is an equilateral polygon. However, it is NOT a regular polygon. For that to be the case, it would also have to be equiangular: that is, all its angles must also be congruent. It is only in the case of triangles that being equilateral implies equiangularity and therefore regularity.

An equilateral polygon is one in which all sides are congruent. The angles may or may not be congruent. The simplest example is an equilateral triangle which must also be equiangular and so is a regular polygon. A rhombus is an equilateral quadrangle. The rhombus, in general, is not regular - only the square (a special type of rhombus) is regular.

Not only can a regular polygon have equal angles and sides, it must have them.

An equilateral polygon is a polygon whose sides are all of the same measure. An equiangular polygon is a polygon whose angles are all of the same measure. A triangle is the only polygon where these two are effectively one and the same.. But it does not apply to polygons of 4 or more sides. A square and rhombus are equilateral but a rhombus is not equiangular. A square and rectangle are equiangular but a rectangle is not equilateral. This can be extended to all polygons with more than 4 sides but it is more difficult because they do not have distinctive names.

Only when it has 3 or more equal sides then it is a regular polygon

No. Regular tessellations use only one polygon. And, according to the strict definition of regular tessellation, the polygon must be regular. Then a tessellation using rectangles, for example, cannot be called regular.

A polygon is an enclosed plane area whose boundaries comprise straight lines. An equilateral polygon is one in which all the sides are of the same length. However, unless it is a triangle, equal sides does not imply equal angles. If, in addition to being equilateral, the polygon is equiangular - that is all its angles are the same - then it is a regular polygon.For example, a rhombus (diamond) is equilateral but the only regular quadrilateral is a square.

Only equiangular and regular hexagons have six equal angles. Hexagons do not have to have six equal angles, and the only way a hexagon can have six equal angles if it is equiangular or regular.

Only if the polygon is a regular quadrilateral.

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