A polygon is a closed plane figure composed of connected line segments with each endpoint intersecting with exactly two other line segments.

Investigate Regular Polygons

1. Click on the link below to explore the characteristics of a regular polygon by dragging the orange dot at one of the vertices to move it around the page. After clicking on the link, click "Make regular" in the upper left hand corner. Answer the questions that follow.

   Polygon

   
   Source: Polygons, Math Open Reference
2. While dragging a vertex around the screen, observe the changes in the polygon. Write your observations and answers to the following questions in your notes.
   
• What happens when the vertex is moved toward the center of the pentagon?
• What happens when the vertex is moved away from the center of the pentagon?
• What do you notice about the sides of the pentagon?
• What do you notice about the angles of the pentagon?
3. Change the number of sides of the polygon and write your observations and answers to the same questions.
4. Write a definition for regular polygons. Use the words "angles" and "sides" in your definition.

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Click here to see a definition for regular polygon.

All the sides and all the angles of regular polygons are equal. All the lines are straight and connected.

Investigate Irregular Polygons

1. Click on the link below to explore the characteristics of an irregular polygon by dragging the orange dot at one of the vertices to move it around the page. Answer the questions that follow.

   Polygon

   
   Source: Polygons, Math Open Reference

2. While dragging a vertex around the screen, observe the changes in the polygon. Write your observations and answers to the following questions in your notes.
• What happens when the vertex is moved toward the center of the pentagon?
• What happens when the vertex is moved away from the center of the pentagon?
• What do you notice about the title above the pentagon when the vertex is moved around the page?
• What does the pentagon look like when it is convex?
• What does the pentagon look like when it is concave?
3. Change the number of sides of the polygon and write your observations and answers to the same questions.
4. Use your answers from the questions above to write a true statement about irregular convex polygons.
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Click here to see a true statement about irregular convex polygons.
All regular polygons are convex and all the vertices point outward. All interior angles are less than 180°

5. Use your answers from the questions above to write a true statement about irregular concave polygons.
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   Click here to see a true statement about irregular concave polygons.

   At least one of the interior angles is greater than 180°. At least one of the interior angles points inward. All the lines are straight and connected.