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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


·        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.