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Polygon that is both equilateral and equilangular?
An equilateral triangle and a square.
A polygon with all sides congruent?
square * * * * * A square is an example, but is not the whole answer. A polygon wit all sides congruent is an equilateral polygon (think equilateral triangle, or a rhombus). If all the angles are also congruent, then it is a regular polygon.
What kind of polygon is an equilateral triangle and a square?
similar
What has all equal sides and all equal angles?
Many different shapes; Square being the most obvious, Equilateral Triangle, Any Regular Polygon
What is a equilateral polygon?
In geometry, an equilateral polygon is a polygon which has all sides of the same length. For instance, an equilateral triangle is a triangle of equal edge lengths. All equilateral triangles are similar to each other, and have 60 degree internal angles. : Any equilateral quadrilateral is a rhombus, which includes the square. : An equilateral polygon which is cyclic (its vertices are on a circle) is a regular polygon. Not all equilateral polygons are convex: all equilateral polygons with more than four sides, such as the pentagon, can be concave. Viviani's theorem holds for equiangular polygons (and also holds for equilateral ones): : The sum of distances from a point to the side lines of an equiangular [or equilateral] polygon does not depend on the point and is that polygon's invariant.
