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Proof in Mathematics Proofs are to mathematics what spelling (or even calligraphy) is to poetry. Mathematical works do consist of proofs, just as poems do consist of characters. Vladimir Arnold
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Standards on Proof Instructional programs that should enable students to:
develop and evaluate mathematical arguments and proofs
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select and use various types of reasoning and methods of proof
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By the end of middle school, students should be able to understand and produce mathematical proofs
Proofs Often proofs are constructed by working backwards. For example: Starting with the desired conclusion T, you could say, "If I could prove statement A, then using previously proved theorem B, I could conclude that T is true." This reduces your proof to proving statement A, then saying at the end of that proof, "Using Theorem B, T is true." Often there are many possibilities for A (and B). The trick is to pick one you can prove!
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Is a method for studying geometry that illustrates congruence and similarity by use of transformations
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Therefore a transformational proof is a proof that employs the use of transformation
Transformation Proof An isometry is a transformation of the plane that preserves length. For example, if the sides of an original pre-image triangle measure 3, 4, and 5, and the sides of its image after a transformation measure 3, 4, and 5, the transformation preserved length. A direct isometry preserves orientation or order - the letters on the diagram go in the same clockwise or counterclockwise direction on the figure and its image. A non-direct or opposite isometry changes the order (such as clockwise changes to counterclockwise).
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