6.1 The Polygon Angle-Sum 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.

Polygons are named based on their number of sides. 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.

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

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