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CME12, 2012.07.02. Rzeszw, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Etvs Lornd University, Budapest

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Gergely Wintsche Outline 1. Dissections, examples 2. The Wallace-Bolyai-Gerwein theorem 3. Cutting a quadrilateral The basic lemma Triangle Trapezoid Quadrilateral Part II / 2 Cut a quadrilateral into 2 halves

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Gergely Wintsche The tangram Part II / 3 Cut a quadrilateral into 2 halves

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Gergely Wintsche The pentominos Part II / 4 Cut a quadrilateral into 2 halves

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Gergely WintschePart II / 5 Cut a quadrilateral into 2 halves Introduction The Wallace-Bolyai-Gerwien theorem

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Gergely WintschePart II / 6 Cut a quadrilateral into 2 halves Introduction The Wallace-Bolyai-Gerwien theorem

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Gergely WintschePart II / 7 Cut a quadrilateral into 2 halves Introduction The Wallace-Bolyai-Gerwien theorem

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Gergely WintschePart II / 8 Cut a quadrilateral into 2 halves Introduction The Wallace-Bolyai-Gerwien theorem

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Gergely WintschePart II / 9 Cut a quadrilateral into 2 halves Introduction The Wallace-Bolyai-Gerwien theorem

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Gergely WintschePart II / 10 Cut a quadrilateral into 2 halves Introduction The basic problem

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Gergely WintschePart II / 11 Cut a quadrilateral into 2 halves Introduction The triangle

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Gergely WintschePart II / 12 Cut a quadrilateral into 2 halves Introduction The quadrilateral

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Gergely WintschePart II / 13 Cut a quadrilateral into 2 halves Introduction The trapezoid

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Gergely WintschePart II / 14 Cut a quadrilateral into 2 halves Introduction Quadrilateral

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Gergely WintschePart II/ 15 Cut a quadrilateral into 2 halves Introduction Solution (1)

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Gergely WintschePart I / 16 Cut a quadrilateral into 2 halves Introduction Solution (2)

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Gergely WintschePart II / 17 Cut a quadrilateral into 2 halves Introduction The quadrilateral