THE POLYGON ANGLESUM THEOREMS

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3-5

• THE POLYGON ANGLE-SUM THEOREMS

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POLYGON

• A CLOSED PLANE FIGURE WITH AT LEAST 3 SIDES THAT
  ARE SEGMENTS WHICH INTERSECT ONLY AT THE END
  POINTS AND NO ADJACENT SIDES ARE COLLINEAR

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POLYGON

• LIES IN 1 PLANE
• AT LEAST 3 SIDES THAT ALL CONNECT AT ENDPOINTS
• NO SIDES INTERSECT

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NAMING A POLYGON

• START AT ANY VERTEX AND LIST THE VERTICES
  CONSECTIVELY IN A CLOCKWISE OR COIUNTER COLCKWISE
  DIRECTION

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EXAMPLE

• EDCBA
• CDEAB
• BAEDC
• ABCDE

E
D
A
C
B
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DIAGONAL

• A LINE THAT ATTACHES 2 NONCONSECUTIVE VERTICIES
  IN A POLYGON

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CLASSIFYING POLYGONS

• CONVEX
• NO DIAGONALS OUTSIDE THE POLYGON

• CONCAVE AT LEAST 1 DIAGONAL OUTSIDE THE POLYGON.

I
H
J
E
A
B
D
L
K
C
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CLASSIFYING BY NUMBER OF SIDES

• NAME
• TRIANGLE
• QUADRILATERAL
• PENTAGON
• HEXAGON
• HEPTAGON

• SIDES
• 3
• 4
• 5
• 6
• 7

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CLASSIFYING BY NUMBER OF SIDES

• NAME
• OCTAGON
• NONAGON
• DECAGON
• DODECAGON
• n-gon

• SIDES
• 8
• 9
• 10
• 12
• n

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SPECIAL POLYGONS

• EQUILATERAL ALL SIDES
• EQUIANGULAR ALL ltS
• REGULAR POLYGON BOTH EQUILATERAL AND EQUIANGULAR

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POLYGON ANGLE-SUM THEOREM

• THE SUM OF THE MEASURES OF THE ANGLES FO AN n-gon
  IS (n 2)180

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POLYGON EXTERIOR ANGLE-SUM THEOREM

• THE SUM OF THE MEASURES OF THE EXTERIOR ANGLES OF
  A POLYGON, ONE AT EACH VERTEX, IS 360.