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Polygons - Problem 1

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

Equiangular polygons have angles congruent to one another. For example, a rectangle is equiangular, since all angles are 90°.

An equilateral polygon is a polygon in which all sides are congruent to one another (or, they all have the same length). A rhombus, for example, is equilateral. However, this does not tell you information about the angles of that polygon.

Regular polygons are both equiangular and equilateral, so all angles in it are congruent and all sides are congruent.

Three words that are related that describe polygons are equiangular, equilateral and regular. But what’s the difference? Well if we look at equiangular if we just look at the word it looks like we have ‘equi’ which means equal to and ‘angular’ which means like it’s similar to the word for angle. And what it means is that all of the angles in a certain polygon are congruent to each other.

So in this hexagon if I told you that it’s equiangular you can assume that all six of these angles must be congruent but that’s it. This doesn’t tell you anything about the length or the sides. The next type will be equilateral.

So let’s say I gave you this quadrilateral and told you that it was equilateral you can assume that the four sides are all congruent to each other. But similar to equiangular you cannot assume anything about the angles. When you put together equilateral and equiangular, you get a regular polygon.

So regular means it is equilateral so you can have all sides congruent and all of your angles are also congruent. So this will be a regular pentagon because it has five sides and all the sides are congruent to each other and all the angles are congruent to each other.

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