1. CME12, 2012.07.02. – Rzeszów, Poland Gergely Wintsche Generalization through problem solving Gergely Wintsche Mathematics Teaching and Didactic Center Faculty of Science Eötvös Loránd University, Budapest

2. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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