Download Chapter 2 Investigating Geometric Figures

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. 2
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. 4
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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5
2
3
6
3
7
8
4
5
4
5
10
7
12
9
6
180 540 108
180 720 120
180 900 128.5
180 1080 135
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10
180 1440 144
180 1800 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)180
n
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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? 12
3. Find the measure of the
missing angle of the quadrilateral.
91°
79°
x
125°
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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. 18
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 # 19
p. 79­80 # 1­4,10­17,19­26
Quiz on
Thursday !!!!
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