DOI QR코드

DOI QR Code

Congruent Triangles Sufficient and Insufficient Conditions Suggested Milestones for Inquiry and Discussion

  • Patkin, Dorit (Mathematical Education, Mathematics Department, Kibbutzim College of Education) ;
  • Plaksin, Olga (Mathematical Education, Mathematics Department, Kibbutzim College of Education)
  • Received : 2009.07.30
  • Accepted : 2011.12.19
  • Published : 2011.12.31

Abstract

In this paper we propose an inquiry task on the subject of congruent triangles. The task deals with conditions that are sufficient for congruency, and conditions that are insufficient. The aim of the task is to find the minimal number of identical components in two triangles that is sufficient to ensure congruency.

Keywords

References

  1. Burke, M. (1990). 5-con triangles. NCTM Student Math Notes 1990(January), 107-112.
  2. Hershkovitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry - or when "a little learning is dangerous thing." In: J. D. Novak (Ed.), Proceedings of the Second International Seminar Misconceptions and Educational Strategies in Science and Mathematics Vol. 3 (pp. 238-251). Ithaca, N Y: Cornell Univ.
  3. Hershkovitz, R. (1998). About reasoning in geometry. In: C. Mammana & V. Villani (Eds.), Perspectives on Teaching Geometry for the 21st Century (pp. 29-37). Dordrecht: Kluwer Academic Publishers.
  4. National Council of Teachers of Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM. ME 1999f.03937 for discussion draft (1998)
  5. Patkin, D. (1994). Drachim l'hitmoded im tayuot nefotsot b'limud geometria (in Hebrew: Methods for dealing with common mistakes in learning geometry). Hachinuch Vesvivo(Seminar Hakibbutzim Press) 16, 113-122.
  6. Patkin, D. (1996). Drachim shonot l'haknayat musagim chadashim b'geometria (in Hebrew: Different methods for imparting new concepts in geometry). Hachinuch Vesvivo(Seminar Hakibbutzim Press) 18, 179-189..
  7. Pawley, R. (1967). 5-con triangles. Mathematics Teacher 60, 438-442.
  8. Van Hiele, P. M. (1986). Structure and Insight. Orlando, FL: Academic Press. ME 1988b.03 491
  9. Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teach. Child. Math. 5(6), 310-316. ME 2000b.01169
  10. Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In: D. Tall (Ed.), Advanced Mathematical Thinking (pp. 65-81). Dordrecht, Netherlands: Kluwer Academic Publishers.