Transcript PRESENTATION NAME - Fay's Mathematics [licensed for non

6.1 The Polygon AngleSum Theorems
Objectives
-Names
-regular polygon
-convex/concave
Polygon – means ‘many angles’
• A few characteristics
-- Each segment intersects exactly 2 other segments
-- No curves
-- All segments are coplanar
-- Figure must be closed
POLYGONS
NOT POLYGONS
• 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.
• A polygon that violates the previous
statement is said to be CONCAVE
Polygons are named based on
their number of sides.
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.
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:
( n  2)180
n
Notice n is the
number of sides,
but it is also the
number of angles.
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
• If you have a polygon with one
interior angle equal to 150. Name
the polygon
• You have a polygon with one interior
angle equal to 144. Name that
polygon.