 #  DEFINITION: closed plane figure formed by 3 or more line segments such that each segment intersects exactly 2 other segments only at endpoints These.

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 DEFINITION: closed plane figure formed by 3 or more line segments such that each segment intersects exactly 2 other segments only at endpoints These figures are not polygonsThese figures are polygons

 DEFINITION: each endpoint of a side of a polygon ◦ Plural is vertices

 Convex: A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon  Non-Convex (concave)- a polygon that is not convex

 Equilateral- polygon with all of its sides congruent  Equiangular- polygon with all of its interior angles congruent  Just like we learned with triangles… but now applies to all polygons!

 Regular- polygon that has all sides and angles congruent  Irregular- two sides or interior angles are not congruent

 Diagonal-segment that joins two nonconsecutive vertices of a polygon

8 Polygon Names 3 sides Triangle 4 sides 5 sides 6 sides 7 sides 8 sides Nonagon Octagon Heptagon Hexagon Pentagon Quadrilateral 10 sides 9 sides 12 sides Decagon Dodecagon n sides n-gon

 The sum of all the exterior angles in a figure is 360. So to find the measure of EACH exterior angle, you divide 360 by the number of sides.  On your chart for n-gon please write under the measure of exterior angle of regular polygon.  Then fill in the rest of the columns.

 Each exterior and interior angle form supplementary angles.  So take 180 – exterior angle to get each interior angle.

 Complete page 2 of your notes by yourself. Then check your answers with the person sitting next to you.

We can divide a polygon into triangles by drawing the diagonals from 1 vertex. Ex. Draw the diagonals from vertex A of pentagon ABCDE. You should have formed 3 triangles. Draw the diagonals from vertex T in the hexagon PQRSTU. You should have formed 4 triangles. Compare the # of sides in the polygon with the # of  s formed. There are 2 fewer  s than sides!!

 Therefore, the sum of all of the (interior) angles of a n-gon is (n - 2)180  So fill in these blanks….  The sum of the angles of a pentagon is _______  180 = __________  The sum of the angles of a hexagon is ________  180 = __________

 Continue working through your note sheet.  If you have questions raise your hand.

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