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Chapter 2

Investigating Geometric Figures

2-2 POLYGONS

Objective: Classify polygons; find the sum of the measures of the interior and exterior angles of polygons

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POLYGON:A closed plane figure

formed by three or more segments that intersect only at their endpoints.

NO GAPS, NO CROSS OVERS

Tell whether the figure is a polygon.

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Each segment that forms a polygon is a side of the polygon.

The common endpoint of two sides is a vertex of the polygon.

A segment that connects any two nonconsecutive vertices is a diagonal.

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You can name a polygon by the number of its sides.

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A polygon is concave if any part of a diagonal contains points in the

exterior of the polygon.

If no diagonal contains points in the exterior, then the polygon is

convex. A regular polygon is always convex.

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All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon.

A regular polygon is one that has all angles and sides are congruent.

If a polygon is not regular, it is called irregular.

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Draw a concave pentagon.

Draw a convex irregular heptagon.

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56781012

579

234

3456810

180180180180180180

540720900108014401800

108120

128.5135144

150

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Theorem 2-3

Polygon Interior Angle-Sum Theorem

The sum of the interior angle measures of a convex polygon with n sides is (n - 2) 180°.

http://www.mathopenref.com/polygoninteriorangles.html

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1. Find the sum of the interior angle measures of a...

convex heptagon.

regular 16­gon.

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In a regular polygon with n sides the measure of one interior angle is

(n - 2)180n

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2. What is each measure of the interior

angle of a regular 18­gon?

What is each interior angle of a dodecogon?

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91°79°

x 125°

3. Find the measure of the missing angle of the quadrilateral.

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In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle

measures is 360°.

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Exterior Angles

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Theorem 2-4

Polygon Exterior Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°.

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4. Find the measure of each exterior angle of a regular 20­gon.

NOTE: One exterior angle of a regular polygon with n sides = 360

n

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5. Find the value of b in polygon FGHJKL.

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6. Ann is making paper stars for party decorations. What is the measure of ∠1?

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7. Find the measure of each interior angle of pentagon

ABCDE. You will have to find the value of c.

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8. The measure of an exterior angle of a regular polygon is 60°. Find the number of sides.

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HW # 19p. 79­80 # 1­4,10­17,19­26

Quiz on Thursday !!!!