Polygons and their angle measures
Definition of a polygon
• A polygon is a closed figure whose sides are line segments that only intersect at their endpoints.
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Polygons and their angle measures
Definition of a polygon
• A polygon is a closed figure whose sides are line segments that only intersect at their endpoints.
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Polygons and their angle measures
Definition of a regular polygon
• In a regular polygon, all the angles have the same measure and all the sides have the same length.
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Polygons and their angle measures
• Polygons can be identified by the number of their sides.
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Polygons and their angle measures
Some of the more common polygons that we will refer to in class this year are: Pentagon ­ five sides
Hexagon ­ six sides
Heptagon ­ seven sides
Octagon ­ eight sides
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Polygons and their angle measures
As we did for two special polygons, (triangles and quadrilaterals), we can develop a method to calculate the angle measures of any polygon.
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Polygons and their angle measures
Let's start with a quadrilateral.
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Polygons and their angle measures
We will draw a diagonal between two opposite vertices.
We form two triangles.
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Polygons and their angle measures
We will draw a diagonal between two opposite vertices.
We form two triangles.
And the angles of the two triangles are included in the original quadrilateral.
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Polygons and their angle measures
A pentagon is a five sided figure. (draw a pentagon in your notes)
We will draw diagonal lines on the pentagon similar to what we did with the quadrilateral.
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Polygons and their angle measures
It would look something like this.
This forms three triangles.
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Polygons and their angle measures
It would look something like this.
This forms three triangles.
And the angles of the three triangles are included in the angles of the original pentagon.
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Polygons and their angle measures
And the angles of the three triangles are included in the angles of the original pentagon.
So using this information, what is the sum of the angle measures of a pentagon?
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Polygons and their angle measures
A hexagon is a six­sided figure.
(draw a hexagon in your notes)
We will draw diagonal lines on the hexagon similar to what we did with the pentagon.
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Polygons and their angle measures
The hexagon diagonals should look like this.
How many triangles did we form?
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Polygons and their angle measures
The hexagon diagonals should look like this.
What is the sum of the angle measures in a hexagon?
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Polygons and their angle measures
An octagon is an 8­sided figure.
(draw an octagon in your notes)
We will draw diagonal lines on the octagon similar to what was done with the pentagon and hexagons
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Polygons and their angle measures
The octagon diagonals should look like this.
How many triangles are formed?
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Polygons and their angle measures
The octagon diagonals should look like this.
What is the sum of the angle measures in an octagon?
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Polygons and their angle measures
Sides
4
Triangles
2
Angle Measure
360
5
3
540
6
4
720
8
6
1080
what we know so far
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Polygons and their angle measures
What would the sum of the angle measures of a 10­sided polygon be?
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Polygons and their angle measures
Sides
4
Triangles
2
Angle Measure
360
5
3
540
6
720
8
4
6
1080
10
8
1440
what we know so far
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Polygons and their angle measures
Sides
4
Triangles
2
Angle Measure
360
5
3
540
6
720
8
4
6
1080
10
8
1440
Can we use these results to help us come up with a general formula that we could use to calculate the sum of angle measures for any polygon?
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