Chapter 6 Polygons
Definitions
• Polygon – many sided figure
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3 sided – triangles
4 sided – quadrilaterals
5 sided – pentagons
6 sided – hexagons
7 sided – heptagons
8 sided – octagons
10sided – decagons
More sides – n gons
Name These Polygons
Octagon
Hexagon
Triangle
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
Regular Polygons
• Regular Polygons – all sides/angles are
congruent to each other
• Each interior angle = 180(n-2)/n
• Each interior angle = 360/n
Example
This is a regular Pentagon
Find the measure of each
Interior Angle
180(n-2)/n = 180(5-2)/5
= 108 deg
Find the measure of each exterior
Angle
360/n = 360/5 = 72
108 72
Example 2
This is a non regular Pentagon
Find the value of x and y
80
70
y
110
x
100
First find the sum of interior
Angles = 180(n-2)
= 180(5-2)
= 540
Then find x : All other angles total
430
540 – 430 = 110
Lastly find y
180 – 110 = 70
Quadrilaterals
• Quadrilaterals have 4 sides
Types of Quadrilaterals
Opposite Sides
ParallelogramsParallel
Rectangles
Rhombuses
Same as Rect.
But ALL sides
Squares
Same as parallelograms,
But all sides
Parallelograms
Opp. Sides parallel
So they’re both Parallelograms
Rhombuses
Squares
What’s in common?
Rhombuses
Opp Sides are parallel
All sides are congruent
They’re both Parallelograms
Give all the possible names of this
Parallelogram
If 4 sides are congruent
Rhombuses
Squares