Classifying Regular and
Irregular Polygons
Kimberly Hopkins
Jen Kershaw
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Printed: April 6, 2016
AUTHORS
Kimberly Hopkins
Jen Kershaw
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C HAPTER
Chapter 1. Classifying Regular and Irregular Polygons
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Classifying Regular and
Irregular Polygons
In this concept, you will learn to identify regular and irregular polygons.
Let’s Think About It
Arletta’s teacher wants the class to identify regular and irregular polygons in the classroom. Arletta missed the
previous day of class when her teacher discussed the definitions of regular and irregular polygons. Arletta measures
her desk and finds that the side lengths are different. She turns to her classmate and asks if she should classify the
polygon as regular or irregular. What should her classmate tell her to write as the classification of the polygon?
In this concept, you will learn to identify regular and irregular polygons.
Guidance
All polygons can be classified as regular or irregular polygons.
A regular polygon is an equilateral polygon where all the side lengths are congruent, and an equiangular polygon
where all the angles are congruent.
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This triangle is a regular polygon. All three side lengths are congruent and all three angles are congruent. Here is an
example of an irregular polygon.
By counting the sides, you can see that this is a five sided figure. It is a pentagon. However, the sides are not
congruent. Therefore, it is an irregular pentagon. Irregular polygons have side lengths that are not congruent.
Guided Practice
Jessie measures one of her bedroom walls and finds that it is 12 feet long. She measures another wall and finds that
it is 10 feet long. The other two walls are also different lengths. Is her room shaped like a regular polygon or an
irregular polygon?
First, determine if all of the lengths are the same.
No
Then, classify the polygon.
Irregular
The answer is an irregular polygon.
Examples
Name each figure as a regular or irregular polygon.
Example 1
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Chapter 1. Classifying Regular and Irregular Polygons
First, look at the sides to see if they look congruent.
Yes
Then, classify the polygon.
Regular polygon
The answer is a regular polygon.
Example 2
First, look at the sides to see if they look congruent.
No
Then, classify the polygon.
Irregular polygon
The answer is an irregular polygon.
Example 3
An octagon with all sides measuring 4 centimeters.
First, determine if all of the sides are congruent.
Yes
Then, classify the polygon.
Regular polygon
The answer is a regular polygon.
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Follow Up
Remember Arleta and her desk? She measured the sides of her desk and found that they were different lengths, but
she doesn’t know if that means that the polygon was regular or irregular. What should her classmate tell her to write
as the classification of the polygon?
First, determine if all of the sides are congruent.
No
Then, classify the polygon.
Irregular
The answer is an irregular polygon. Her classmate should tell her to write that it is an irregular polygon.
Explore More
Based on each description, determine whether the polygon is regular or irregular.
1. A quadrilateral with all sides equal to 5 cm and all right angles.
2. A pentagon with different side lengths.
3. A square.
4. A rectangle.
5. An octagon with one side that is 8 cm and the other sides congruent to that side. All angles are congruent.
6. A heptagon with seven congruent sides and angles.
7. A hexagon with six congruent angles.
8. A hexagon with the following side lengths: 4 m, 5 m, 7 m, 5 m, 4 m and 7 m.
9. A pentagon with five congruent angles.
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Chapter 1. Classifying Regular and Irregular Polygons
10. True or false. A figure can be a polygon and be regular or irregular.
Identify each polygon below.
11. a
12. b
13. c
14. d
Now tell whether each is regular or irregular.
15. a
16. b
17. c
18. d
Answers for Explore More Problems
To view the Explore More answers, open this PDF file and look for section 9.13.
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