Ms. Jennifer Swanson & Ms. Amanda Phifer

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Presentation transcript:

Ms. Jennifer Swanson & Ms. Amanda Phifer Polygons Ms. Jennifer Swanson & Ms. Amanda Phifer

What is a polygon? A Polygon is a shape that is a closed plane figure where All line segments are straight Lines don’t cross or use end points more than once Only consists of outer shape, not inner area Regular Polygons are EQUILATERAL and EQUANGULAR

A regular polygon… All angles and sides are equal! If not, then is irregular Vertices are corner points on a polygon. Irregular Regular

Angles Angles total greater than 180 degrees Convex Concave Angles total greater than 180 degrees Has reflex angles Caves in Angles total to 180 degrees or less Flex out

What do polygons look like?

360 degree angles Total, 90 deg. each Triangle Quadrilateral 4 sided figure, 4 angles 360 degree angles Total, 90 deg. each 4 vertices, 1 diagonal from single vertex 3 sided figure, 3 angles 180 deg. angles Total, 60 deg. each 3 vertices, 0 diagonals from single vertex

540 deg. angles Total, 108 deg. each Pentagon Hexagon 5 sided figure, 5 angles 540 deg. angles Total, 108 deg. each 5 vertices, 2 diagonals from single vertex 6 sided figure, 6 angles 720 deg. angles Total, 120 deg. each 6 vertices, 3 diagonals from single vertex

900 deg. angles Total, 128.57 deg. each Heptagon Octagon 7 sided figure, 7 angles 900 deg. angles Total, 128.57 deg. each 7 vertices, 4 diagonals from single vertex 8 sided figure, 8 angles 1080 deg. angles Total, 135 deg. each 8 vertices, 5 diagonals from single vertex

Angles and Diagonals in Regular Polygons Example: Octagon S=8 D=(8-3)=5 T=(8-3)+1=6 6 (T)x 180= 1080 degrees total 1080 degrees/ 8 angles= 135 degrees per angle Side (S) = X Diagonal (D) = (X-3) Triangle (T) = {(X-3)+1} (X-2) 135 degree angle 180 degree (straight line)-135 degrees (interior angle)= 45 degrees (exterior angle)

1260 deg. angles Total, 140 deg. each Nonagon Decagon 9 sided figure, 9 angles 1260 deg. angles Total, 140 deg. each 9 vertices, 6 diagonals from single vertex 10 sided figure, 10 angles 1440 deg. angles Total, 144 deg. each 10 vertices, 7 diagonals from single vertex

Sources http://www.mathleague.com/help/geometry/polygons.htm http://www.math.com/school/subject3/lessons/S3U2L1GL.html http://www.mathsisfun.com/geometry/polygons.html Grandfather Tang’s Story (A Tale With Tangrams) by Ann Tompert