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Transcript
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.