Lesson 1: Similar Polygons - Regular Polygons

   Constructing Knowledge

In addition to triangles there is another special circumstance that leads to a shortcut in determining similarity. Regular polygons with the same number of sides are similar. A regular polygon is defined as any polygon whose side lengths and angles measures are identical. When determining if two polygons are similar, a good first step is to determine if the polygons are regular.

Determining if a Polygon is a Regular Polygon
  1. Look to see if labels show that angles are the same. A single arc for an angle indicates that the angle measure is the same measure as any other angle with a single arc. Look for a difference in the number of arcs. Single and double arcs in the same polygon mean the angle measures are different and the polygon is not regular.
  1. Look to see if labels show that the side lengths are all the same. A single hash mark for a side length indicates that the side length is the same length as any other side with a single hash. Look for a difference in the number of hash marks. Single and double hash marks in the same polygon mean the side lengths are different and that the polygon is not regular.

  1. Read the question carefully to see if the wording tells that all side lengths/angle measures are the same.

Here are some common regular polygons:



Notice that in these diagrams all the hash marks and arcs are singles, indicating that they are regular polygons.

EXAMPLE 1

Are the following polygons similar?



Solution


Yes, these octagons are similar. Both have 8 sides of equal length and 8 equal angle measures. They are both regular octagons. Because both octagons are regular polygons, they are similar. There is no need to compare corresponding side length ratios.

EXAMPLE 2

Are the following polygons similar?



Solution


No, these hexagons are not similar. The first hexagon has two sides that are different lengths, whereas the second hexagon is regular. The corresponding side length ratios would be different for the top and bottom sides.


Now, it is your turn! Complete the questions in your Chapter 8, Lesson 1 Practice Makes Perfect that refer to Regular Polygons.



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