6.1 The Polygon Angle-Sum Theorems

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6.1 The Polygon Angle-Sum Theorems

• Objectives
• -Names
• -regular polygon
• -convex/concave

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Polygon means many angles

• A few characteristics

-- Each segment intersects exactly 2 other
segments
-- No curves
-- All segments are coplanar
-- Figure must be closed
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POLYGONS
NOT POLYGONS
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• Convex Polygon polygon such that no line
  containing a side of the polygon contains a point
  in the interior of the polygon.
• Extend each side of the polygon, if no part of
  the extended LINE lies inside the polygon then it
  is convex.

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• A polygon that violates the previous statement is
  said to be CONCAVE

Polygons are named based on their number of
sides.
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Title

• Diagonal ? a segment joining two nonconsecutive
  vertices of a polygon.
• To help find out how many degrees are in any
  polygon, you can draw diagonals from one vertex
  and construct many triangles.

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Theorem

• The sum of the measure of the interior angles of
  a convex polygon with n sides is (n-2)180.
• To find the value of ONE INDIVIDUAL interior
  angle of a REGULAR POLYGON you use this formula

Notice n is the number of sides, but it is also
the number of angles.
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Theorem

• The sum of the measures of the exterior angles of
  any convex polygon, one angle at each vertex is
  360.

• Exterior angle measurement applet

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• If you have a polygon with one interior angle
  equal to 150. Name the polygon

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• You have a polygon with one interior angle equal
  to 144. Name that polygon.