Chapter 6 Polygons

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Chapter 6 Polygons
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Definitions

• Polygon many sided figure
• 3 sided triangles
• 4 sided quadrilaterals
• 5 sided pentagons
• 6 sided hexagons
• 7 sided heptagons
• 8 sided octagons
• 10sided decagons
• More sides n gons

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Name These Polygons
Octagon
Quadrilateral
Hexagon
Triangle
Pentagon
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Polygon Formulas

• Interior angles
• The sum 180(n-2) n is number of sides
• Exterior angles
• The sum 360 degrees

Any adjacent Interior and Exterior Angles are
supplementary Because they form a straight line
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Regular Polygons

• Regular Polygons all sides/angles are congruent
  to each other
• Each interior angle 180(n-2)/n
• Each interior angle 360/n

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Example
Find the measure of each Interior
Angle 180(n-2)/n 180(5-2)/5
108 deg
This is a regular Pentagon
Find the measure of each exterior Angle 360/n
360/5 72
108
72
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Example 2
This is a non regular Pentagon
Find the value of x and y
80
First find the sum of interior Angles 180(n-2)
180(5-2) 540
y
70
x
110
100
Then find x All other angles total
430 540 430 110
140
110
Lastly find y 180 110 70
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Quadrilaterals

• Quadrilaterals have 4 sides

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Types of Quadrilaterals
Parallelograms
Opposite Sides Parallel
Opp. Sides All rt Opp. Sides
Rhombuses
Rectangles
Same as parallelograms, But all sides
Same as Rect. But ALL sides
Squares
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Parallelograms
Opp. Sides parallel
So theyre both Parallelograms
Whats in common?
Rhombuses
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Squares
Rhombuses
Whats in common?
Opp Sides are parallel
All sides are congruent
Theyre both Parallelograms
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Give all the possible names of this Parallelogram
Rhombuses
If 4 sides are congruent
Squares