Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 DIRT Identify the relation of the angle pairs: 1) <1 and <9 ____________ 2) <2 and <7 ____________ 3) <7 and <11 _____________ 4) <9 and <16 ____________ 5) <1 and <4 ______________ 6) <6 and <11______________ 7)<9 and <11_______________ 8) Find the value of x to prove l // m 55 l x+25 m 1 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 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 2 Chapter 3.4 Polygons Day 1 .notebook October 30, 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. examples: counter­example: 3 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Polygons # of sides type 3 4 5 6 7 8 9 10 n 4 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Naming a polygon­ Start at any vertex and list vertices consecutively. A R L B G E List the vertices: List the sides: List the angles: Name: ALGEBR 5 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Concave: when any part of the diagonals fall on the outside of the polygon. Hmmmmmm ... Can a triangle be convex? Concave??? Why?? 6 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Remember equiangular?? What about equilateral? When a polygon is both equiangular AND equilateral, we call it REGULAR. 7 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Classify the polygon. Use three words if possible. Ex 1) Ex 2) Ex 3) Ex 4) 8 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Classify the polygon. Use three words if possible. Ex 5) Ex 6) Ex 7) 70 70 9 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Sketch the polygon if possible. Ex 8) Regular hexagon Ex 9) Equilateral right triangle Ex 10) Concave equiangular qualdrilateral 10 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Exploration: Triangles and polygons Using the dot paper provided, work with your desk partner and sketch each polygon. 11 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Fill out the chart on your paper. Type of # of sides # of triangles Sum of the interior angles polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon 12 Chapter 3.4 Polygons Day 1 .notebook October 30, 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) 13 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 Worksheet Guide for p147-150 1-10, 55, 71-73, 80-86 1. Is the figure a polygon?______ If not, why? ___________________________________________ 2. Is the figure a polygon?______ If not, why? ___________________________________________ 3. Is the figure a polygon?______ If not, why? ___________________________________________ 4. Is the figure a polygon?______ If not, why? ___________________________________________ 5. Name of polygon: ___________________ 6. Name of polygon: ___________________ Sides: ___________________________ Sides: ___________________________ ___________________________ ___________________________ Angles: __________________________ Angles: __________________________ __________________________ __________________________ 7. Name of polygon: ___________________ 8. Classify by sides: _______________ Sides: ___________________________ Convex or concave? _____________ ___________________________ Angles: __________________________ 9. Classify by sides: _______________ __________________________ Convex or concave? _____________ 10. Classify by sides: _______________ Convex or concave? _____________ 55. Provide 4 sentences to describe the figure. _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________ 14 Chapter 3.4 Polygons Day 1 .notebook October 30, 2013 71. Work: ____________________ 72. Work: ____________________ y= ____________________ x= ____________________ 73. Work: ____________________ 80. opposite rays: ________________________ 81. two right angles: ______________________ 82. two segments: _______________________ x= ____________________ 83. an acute angle: _______________________ y= ____________________ 84. an obtuse angle: ______________________ 85. a straight angle: ______________________ 86. a midpoint: _________________________ 15.