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Does a equiangular triangle have to be equilateral?
No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral
What does equilateral and equiangular mean?
The terms equiangular means a polygon having the same angle between any two adjacent sides. Equilateral means all sides of equal length. A polygon can be equilateral without being equiangular (the rhombus) and equiangular without being equilateral (the rectangle). If a polygon is both equilateral and equiangular, it is a "regular polygon" such as the pentagon, square, and equilateral triangle.
When is an equilateral triangle not equiangular?
If a triangle is equiangular, it will have all equal angles. So, it might be similar to another equiangular triangle, but not congruent. It is not equilateral if the sides are not equal in length. All equiangular triangles are similar, but not all of them are congruent, which means they do not all have corresponding side lengths. But, all equilateral triangles are equiangular.
Is a triangle a small regular polygon?
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).
What figures is not always equilateral square rhombus or rectangle?
A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.
