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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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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 !!!!
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