# What is an equiangular polygon?

Asked by rentluva5256 (550 ) January 29th, 2010

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A good trick is to dissect the word you don’t know the definition of, so in this case, equiangular. Equi = equal, angle is referring to the angles. Thus an equiangular polygon is any polygon where all the angles contain the same number of degrees.

@fireinthepriory I thought that was what an equilateral polygon was.

rentluva5256 (550 )

Fireinthepriory is right.

“A polygon having all its angles equal is called Equiangular Polygon.”
From:
http://www.icoachmath.com/sitemap/Equiangular_Polygon.html

http://en.wikipedia.org/wiki/Equiangular_polygon

Just to have it from multiple sources.
-Dan

Dan_DeColumna (2420 )

@rentluva5256 Well, equilateral technically means all the sides are the same lengths. Due to the way shapes and angles work, anything that is equilateral is also equiangular, and vice versa. Imagine having all the sides locked in at the same length, the angles cannot change and will all be equal to one another.

Oh. So equilateral means all the sides are equal, but equiangular means all of the angles are equal?

rentluva5256 (550 )

Ok. Well here’s another question. What if the polygon is both? (Sorry if I’m asking too much!)

rentluva5256 (550 )

A polygon that is one of the two would be both. You can visualize it better if you make shapes with some toothpicks, all of which are the same length.

Dan_DeColumna (2420 )

I was gonna say a square, but I reckon that isn’t the only shape which satisfies all criteria.

aprilsimnel (30581 )

Oh. How about if it was neither? Is that regular?

rentluva5256 (550 )

Actually, thinking about it, I’m wrong. A parallelogram is equilateral, but not equiangular.

Dan_DeColumna (2420 )

Shapes with toothpicks is a GREAT idea.

@rentluva5256 Many polygons will be both or neither. Anything equiangular will by necessity be equilateral, but shapes can be equilateral but not equiangular. Yeah, @Dan_DeColumna, I just remembered shapes that are equilateral but not equiangular, too… D’oh! It’s been too long…

@fireinthepriory it’s alright. I just didn’t want to steer the guy wrong. Good clarification there, by the way.

Dan_DeColumna (2420 )

Wait. What is a regular polygon? (by the way, @Dan_DeColumna , I’m a girl. Just saying.)

rentluva5256 (550 )

@rentluva5256: Sorry about that, no offense intended. I could be wrong, but if the sex is undetermined, isn’t it proper grammar to default to male pronouns?

Dan_DeColumna (2420 )

Haha. I don’t know. But what is a regular polygon!?!?!?!

rentluva5256 (550 )

A regular polygon is a polygon which is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). They’re basically the building blocks of the elementary shapes you learned as a small child.

Here’s a picture:

http://mathforum.org/sum95/math_and/poly/reg_polygons.html

Hope that helps,
-Dan

Dan_DeColumna (2420 )

Thank you sooooooo much!

rentluva5256 (550 )

Dan_DeColumna (2420 )

Equilateral does not imply equiangular. A square can be ‘leaned over’ to make a rhombus with two distinct angles. Likewise a regular hexagon can be squashed to produce unequal angles while maintaining equal sides.

Equiangular does not imply equilateral. A square can be stretched into a rectangle, & a regular hexagon can be stretched along a pair of opposite sides, while remaining equiangular.

A regular polygon is both equilateral and equiangular.

gasman (10726 )

Thanks for putting that clearly @gasman. Both @fireinthepriory and myself recalled that belatedly.
-Dan

Dan_DeColumna (2420 )

or