Repository of recommendations and tips

# Can you have an equiangular but not equilateral?

## Can you have an equiangular but not equilateral?

For instance, in the case of quadrilaterals, a rectangle is equiangular but not equilateral, while a rhombus is equilateral but not equiangular. If n is even, then it is possible to have an n-gon with all opposite sides parallel.

## Do all regular polygons have equilateral?

All regular polygons and edge-transitive polygons are equilateral. An equilateral quadrilateral must be convex; this polygon is a rhombus (possibly a square).

Is an equiangular Pentagon always equilateral?

In geometry, an equilateral pentagon is a polygon in the Euclidean plane with five sides of equal length. In contrast, the regular pentagon is unique, because it is equilateral and moreover it is equiangular (its five angles are equal; the measure is 108 degrees).

Do all regular polygons equiangular?

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.

### Which of the following is an equiangular but not equilateral polygon?

Here is one example of a pentagon that is equiangular but not equilateral.

### Do all Equiangular polygons equilateral if no give a counterexample?

In the case of triangles, being equiangular requires that the triangle also be equilateral. Thus, not all equiangular quadrilaterals are equilateral and so are not all regular.

Do all Equiangular polygons equiangular?

That is, every equiangular triangle is a regular triangle. However, this is not the case for all polygons. For example, a rectangle is equiangular — all four angles are 90° — but need not be square (need not have all four sides the same length).

Are equiangular and equilateral the same?

For example, equilateral triangles have all congruent sides – that’s the definition of equilateral. All their angles are the same also, which makes them equiangular. For triangles, it turns out that being equilateral and equiangular always go together.

#### What quadrilateral if any is equilateral but not regular equiangular but not regular?

A quadrilateral can be equiangular but not equilateral (a rectangle) or equilateral but not equiangular (a rhombus). A square, however, is both. All sides of a square are the same length (equilateral) and all its angles have the same measure (equiangular).

#### Are all equiangular hexagons equilateral?

It is easy to prove that all equiangular triangles are also equilateral using basic trogonometric rules. On the other hand, it is easy to conceive of an equiangular quadrilateral that is not equilateral, i.e. a rectangle.

Can a polygon be equiangular but not?

What is equiangular polygon?

In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths.