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### Chapter 9--The Pythagorean Theorem

 Essential Question:  How can the Pythagorean Theorem be applied to real-world situations? Unit Rationale:  Understanding of the Pythagorean Theorem can be applied to engineering design, constructions, and navigation. As a result of this unit, students will be able to: Ø  Apply the Pythagorean Theorem and its converse to: §  Real world situations §  Finding distance on a coordinate grid §  Circles Vocabulary: ·        Pythagorean Theorem ·        Special Triangles ·        Distance formula ·        Converse ·        Inverse ·        Contrapositive ·        Validity ·        Counterexample 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.3.C  Use the properties of special triangles to solve problems. *G.3.D  Know, prove, and apply the Pythagorean Theorem and its converse. G.4.D  Determine the equation of a circle that is described geometrically in the coordinate plane, and , given equations for a circle and a line, determine the coordinates of their intersection(s). Supporting Standards: *G.1.C  Use deductive reasoning to prove that a valid geometric statement is true. 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.D  Write the converse, inverse, and contrapositive of a valid proposition, and determine their validity. 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.F  Summarize mathematical ideas with precision and efficiency for a given audience and purpose.