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GPS Alignment Course WEEK 13: GEOMETRY – POLYGONS Tessellation Restrictions Can any triangle be used to make a tessellation? Can any quadrilateral be used to make a tessellation? Can any polygon be used to make a tessellation? Why or why not? Summarize your findings. GPS M6G1. Students will further develop their understanding of plane figures. a. Understand the meaning of line and rotational symmetry. As seen in Problem Exploration In order to solve this problem, the students will have to have an understanding of what tessellate means - rotating about one point such that there are no overlaps or gaps.! M7G1. Students will construct plane figures that meet given conditions. They will also demonstrate understanding of transformations. b.! Demonstrate understanding of translations, symmetry, dilations, rotations and reflections. ! M8G1. Students will analyze and use characteristics and properties of geometric figures. c.! Use and apply the properties of triangles and parallelograms. ! To find out which polygons tessellate, the student can use either GSP, an applet, or cut out various shapes from paper to see which ones tessellate by actually rotating the shape about a given point.!Some triangles tessellate through reflection, some rotation. Not all polygons tessellate and using what is known about certain polygons can help determine which do. If a triangle is rotated about the midpoint of one of the sides, then a parallelogram is formed. 1 GPS Alignment Course Sum of Angles in a Polygon What is the sum of the angles of a triangle? of a quadrilateral? of a pentagon? of a hexagon? What is the sum of the angles in convex polygons in terms of the number of sides? GPS M6G1. Students will further develop their understanding of plane figures. As seen in Problem Exploration The definition of convex and nonconvex polygons will need to be understood.! Then various convex polygons will need to be constructed. M6A2. Students will consider relations between varying quantities. a. Analyze and describe patterns arising from function rules, tables, and graphs. Have the students create table with the columns: Polygon, #of Sides, #of Triangles, Sum of Degrees.!!The pattern can be generalized to (n-2) *180. M7A3. Students will understand relations and functions. a.!Graph coordinates in a plane. b.!Represent, describe and analyze a functional relation from a table, graph, and/or formula. The students create a table with the number of sides of a polygon in one column and the corresponding angle sum in the other.! Plot the points.! The relationship is linear and is represented as y = 180x -360. M8A3. Students will graph and analyze graphs of linear equations. b.! Graph equations of the form y = mx + b. d. Determine the equation of a line given a graph or data. e.!Interpret the meaning of the slope and yintercept in a given situation. Extending from the above description, the students will need to determine that the relationship is linear, and determine the equation by finding the slope from 2 of the points, and then the y-intercept. M8G1. Students will analyze and use characteristics and properties of geometric figures. c. Use and apply the properties of triangles and parallelograms. The!sum of angles of a triangle is 180 degrees and the polygons that aren't triangles can be broken into triangles.!Therefore, a relationship between the number of sides of a polygon can be generalized. 2