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Standards/Math/Minnesota/9.3.2

9.3.2

9.3 Geometry & Measurement
9.3.1
9.3.2
9.3.2.19.3.2.29.3.2.39.3.2.49.3.2.5
9.3.3
9.3.4

Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.

9.3.2.1Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.9.3.2.2Accurately interpret and use words and phrases such as ''if...then,'' ''if and only if,'' ''all,'' and ''not.'' Recognize the logical relationships between an ''if...then'' statement and its inverse, converse and contra positive.9.3.2.3Assess the validity of a logical argument and give counterexamples to disprove a statement.9.3.2.4Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations.9.3.2.5Use technology tools to examine theorems, make and test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.
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