1.6 Classifying Polygons Polygon: ! A closed plane figure ! Formed by three or more line segments, called sides. ! Each side intersects two other sides at the endpoints, nowhere else. ! No two sides sharing an endpoint are collinear. ! The endpoint of a side is called a vertex. ! (Vertices is the plural form.) Concave vs. Convex (Non convex) Every diagonal is in the interior of the figure. !Diagonal: a segment connecting two non consecutive vertices. !Consecutive: one right after the other. A rubber band fits the exact shape of a convex polygon. A concave polygon is “caved” in and will not have the same shape as the rubber band placed around it. Not a polygon: Not closed convex concave concave convex no sides Not a plane figure List all the polygons you can name; include the number of sides. ! 3 triangle 30 sides: ! 4 quadrilateral 30-gon ! 5 pentagon 19 sides: ! 6 hexagon 19-gon ! 7 heptagon 108 sides: ! 8 octagon 108-gon ! 9 nonagon ! 10 decagon When you are asked to “classify a polygon,” ! 11-gon you are expected to give one of these names. ! 12 dodecagon ! N n-gon Classify these polygons. pentagon Dodecagon Heptagon quadrilateral Equilateral: Having sides of equal length. Equiangular: Having angles of equal measure. Regular: Both equilateral and equiangular. Are any of the above figures equilateral, equiangular, or regular? How can we know? These hatch marks indicate sides of equal length. Classify the polygon shown at the right by the number of sides. Explain how you know that the sides of the polygon are congruent and that the angles of the polygon are congruent. Regular quadrilateral Four sides of equal length (equilateral.) Four angles that are each 90 degrees (equiangular.) ALGEBR A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side. SOLUTION 3x + = 4x – Write equation. 6 = x – Subtract 3x from each side. 8 = x Add 2 to each side. Then find a side length. Evaluate one of the expressions when x = 8. 3x + = 3(8) + = 3 ANSWE The length of a side of the table is 30 Geometry ! Page 44(2-7, 8-16 ev, 18-23,24-30 ev, 33-36) ! There is only one section left in chapter one. Begin studying for the test over the whole chapter. There have been a lot of new definitions and concepts..