Presentation on theme: " DEFINITION: closed plane figure formed by 3 or more line segments such that each segment intersects exactly 2 other segments only at endpoints These."— Presentation transcript:
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
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.