section 3-5 angles of a polygon. polygon means: “many-angled” a polygon is a closed figure...

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Section 3-5 Angles of a Polygon

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Page 1: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Section 3-5Angles of a

Polygon

Page 2: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Polygon

• Means: “many-angled”

• A polygon is a closed figure formed by a finite number of coplanar segments

a. Each side intersects exactly two other sides, one at each endpoint.

b. No two segments with a common endpoint are collinear

Page 3: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Ex #1

Examples of polygons:

Ex#2

Page 4: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Two Types of Polygons:

1. Convex: If a line was extended from the sides of a polygon, it will NOT go through the interior of the polygon.

Ex #1

Page 5: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

2. Nonconvex: If a line was extended from the sides of a polygon, it WILL go through the interior of the polygon.

Ex#2

Page 6: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Polygons are classified according to the number of sides they have.

*Must have at least 3 sides to form a polygon.

Special names

for Polygons

Number of Sides

Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

n n-gon*n stands for number of sides.

Page 7: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Diagonal

• A segment joining two nonconsecutive vertices

*The diagonals are indicated with dashed lines.

Page 8: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Definition of Regular Polygon:

• a convex polygon with all sides congruent and all angles congruent.

Page 9: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Interior Angle Sum Theorem

• The sum of the measures of the interior angles of a convex polygon with n sides is

S = 180 (n - 2)

Page 10: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

One can find the measure of each interior angle of a regular polygon:

1. Find the Sum of the interior angles

2.Divide the sum by the number of sides the regular polygon has.

S = 180 (n - 2)

n

S

Page 11: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

One can find the number of sides a polygon has if given the measure of an interior angle

n

n 2180

Page 12: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

Exterior Angle Sum Theorem

• The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.

Page 13: Section 3-5 Angles of a Polygon. Polygon Means: “many-angled” A polygon is a closed figure formed by a finite number of coplanar segments a.Each side

One can find the measure of each exterior angle of a regular polygon:

360

n = exterior angle

or

360

exterior angle = n

One can find the number of sides a polygon has if given the measure of an exterior angle