6.1 Vocabulary Side of a polygon Vertex of a polygon Diagonal Regular polygon Concave convex

6.1 Properties & Attributes of Polygons Geometry

Polygon Polygon- a plane figure that (1) is formed by 3 or more segments, such that no two sides with a common endpt are collinear and (2) each side intersects exactly 2 other sides , 1 at each endpt. Means the figure is closed and no sides cross over each other. Vertex- the endpts of each side Think of them as the corner points!

For Ex. vertex side

Ex. 1 Is the figure a polygon? yes yes no no

KNOW THIS!!!!!!!!!!!! Number of sides 3 Type of polygon Triangle 4 5 6 7 8 9 10 12 n Type of polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon N-gon

Special types of Polygons Convex- no line that contains a side of a polygon goes through its interior Concave- any part of a diagonal contains points from the exterior of the polygon Equilateral- all sides are  Equiangular- all angles are  Regular polygon- equilateral and equiangular (convex) (A regular polygon is always convex.)

Ex. 2 regular? ( ) ( )) ) ( ( (( yes NO! NO!

Diagonals A (ie segments AE and AD) C B D E Diagonal- a segment that joins 2 nonconsecutive vertices A (ie segments AE and AD) C B D E

Thm 6-1-1 Polygon Angle Sum Theorem The sum of the interior angle measures of a convex polygon with n sides is (n-2)180

Polygon # of sides # of triangles Sum of interior angle measures Triangle 3 1 180 Quadrilateral 4 2 360 Pentagon 5 540 Hexagon 6 720 n-gon n n-2 (n-2)180

Interior  ‘s of a quad B A 1 2 m1+m2+m3+m4=360o 3 4 D C The sum of the measures of the interior ‘s of a quad =360o. B A 1 2 m1+m2+m3+m4=360o 3 4 D C

Ex. 3 Find x ( X x+x+55+55=360 2x+110=360 2x=250 X=125 55o ) X

Ex. 4 A. Find the sum of the interior angle measures of a convex heptagon. B. Find the measure of each interior angle of a regular 16-gon. C. Find the measure of each interior angle of pentagon ABCDE. Ex.3

Assignment