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### Chapter 5--Discovering Polygon Properties

 Essential Question:  How can the properties of polygons be used to identify and prove theorems? Unit Rationale:  Extending the properties and theorems of triangles to convex polygons expands our ability to prove and apply conjectures about a wider number of two-dimensional physical shapes and prepare us for future applications of three-dimensional shapes, such as prisms and pyramids. As a result of this unit, students will be able to: Ø  Determine the sum of the measures of the interior angles of any polygon and the measure of each angle in a regular polygon. Ø  Apply the knowledge that the sum of the exterior angles of a polygon is constant at 360 degrees. Ø  Identify, prove, and apply the properties of general and special quadrilaterals. Vocabulary: ·        Quadrilateral ·        Kite ·        Trapezoid ·        Parallelogram Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements.  Focus Standards: G.2.A  Know, prove, and apply theorems about parallel and perpendicular lines. G.2.B  Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal. *G.3.F  Know, prove, and apply basic theorems about parallelograms. *G.3.G  Know, prove, and apply theorems about properties of quadrilaterals and other polygons. G.4.A  Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a give point parallel to a given line, and a line through a given point perpendicular to a given line. *G.4.B  Determine coordinates of a point that is described geometrically. Supporting Standards: G.1.B  Use inductive reasoning to make conjectures, to test the plausibility of a geometric statement, and to help find a counterexample. *G.1.C  Use deductive reasoning to prove that a valid geometric statement is true. *G.4.C  Verify and apply properties of triangles and quadrilaterals in the coordinate plane. Reasoning, Problem Solving, and Communication Standards: G.7.D  Generalize a solution strategy for a single problem to a class of related problems and apply a strategy for a class of related problems to solve specific problems. *G.7.G  Synthesize information to draw conclusions and evaluate the argument and conclusions of others.