Interior Angles of Polygons

Author:Vanessa

The side lengths and angles for Triangle ABC are given. Move the points around to adjust them in any way that you would like. What do the interior angles always add up to?

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Move the points around on triangle DEF. What's a similarity between this triangle and the one above? What are a few differences?

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On both of these 4-sided polygons, move the points around in any way you want. What is one similarity and one difference between the green and purple polygon?

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Move the sliders so that

and

are at 0 degrees. Notice that the purple square is made up of two triangles (each is 180 degrees)

Move the points in this 5-sided polygon around. What do the angles add up to?

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How many triangles can we make using a 5-sided polygon? How is this related to the above question about the interior angles?

Compare the green 5-sided polygon to this purple 5-sided polygon. What is similar about these two? What is different?

We call a polygon a "regular polygon" whenever all sides are equal and all angles are equal, like in this above example.

Move the sliders so that

, and

are all at 0 degrees. Notice that this pink polygon is made up of three triangles. We can confirm that a 5-sided polygon is made up of three triangles.

Based on the information given in this picture, is this green 6-sided polygon considered a regular polygon?

Last Question! How many triangles can we make out of a 6-sided polygon? How is this related to the total sum of the interior angles?

Interior Angles of Polygons

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