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Transcript
Chapter 3.4 Polygons Day 1.notebook February 07, 2013 Polygon A closed plane figure with at least 3 sides that are segments. The sides intersect only at their endpoints and no adjacent sides are collinear. 3.4 The Polygon AngleSum Theorems Objective: To classify polygons To find the sums of the measures of the interior and exterior angles of polygons M.2.B. Performance Standard 3.6 DOK1 Knowledge MA 3 counterexample: examples: Aug 46:47 AM Aug 46:48 AM Polygons Diagonals: a segment drawn from one vertex to any other non consecutive vertex # of sides type 3 4 5 6 7 Convex: when all diagonals lie on the insode of the polygon 8 9 10 n Aug 46:52 AM Concave: when any part of the diagonals fall on the outside of the polygon. Aug 47:00 AM Naming a polygon Start at any vertex and list vertices consecutively. A L R B G E List the vertices: List the sides: List the angles: Name: ALGEBR Hmmmmmm ... Can a triangle be convex? Concave??? Why?? Aug 47:02 AM Aug 47:46 AM 1 Chapter 3.4 Polygons Day 1.notebook February 07, 2013 Classify the polygon. Use three words if possible. Ex 1) Ex 2) Ex 3) Ex 4) Remember equiangular?? What about equilateral? When a polygon is both equiangular AND equilateral, we call it REGULAR. Aug 47:05 AM Aug 47:10 AM Classify the polygon. Use three words if possible. Sketch the polygon if possible. Ex 6) Ex 5) Ex 8) Regular hexagon Ex 9) Equilateral right triangle Ex 7) 70 70 Ex 10) Concave equiangular qualdrilateral Aug 47:13 AM Aug 47:18 AM Exploration: Triangles and polygons Using the dot paper provided, work with your desk partner and sketch each polygon. Fill out the chart on your paper. Type of polygon # of sides # of triangles Sum of the interior angles triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon Aug 47:30 AM Aug 47:31 AM 2 Chapter 3.4 Polygons Day 1.notebook February 07, 2013 What conjectures can you make about the relationship between the number of sides of a polygon and the sum of the interior angles (1st and 4th column)? (Hint: think about patterns) Aug 47:41 AM Feb 712:20 PM 3