• Title/Summary/Keyword: Congruent conditions of triangles

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

  • Patkin, Dorit;Plaksin, Olga
    • Research in Mathematical Education
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    • v.15 no.4
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    • pp.327-340
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    • 2011
  • 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.

A Study on the Comparison of Triangle Congruence in Euclidean Geometry (유클리드 기하학에서 삼각형의 합동조건의 도입 비교)

  • Kang, Mee-Kwang
    • The Mathematical Education
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    • v.49 no.1
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    • pp.53-65
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    • 2010
  • The congruent conditions of triangles' plays an important role to connect intuitive geometry with deductive geometry in school mathematics. It is induced by 'three determining conditions of triangles' which is justified by classical geometric construction. In this paper, we analyze the essential meaning and geometric position of 'congruent conditions of triangles in Euclidean Geometry and investigate introducing processes for them in the Elements of Euclid, Hilbert congruent axioms, Russian textbook and Korean textbook, respectively. Also, we give justifications of construction methods for triangle having three segments with fixed lengths and angle equivalent to given angle suggested in Korean textbooks, are discussed, which can be directly applicable to teaching geometric construction meaningfully.

A Comparative Study on Contents Related with 'Congruence of Triangles' of Korean and Russian Mathematics Textbooks (한국과 러시아의 수학교과서에 제시된 '삼각형의 합동'에 관련된 학습내용의 비교 연구)

  • Han, In-Ki
    • Journal of the Korean School Mathematics Society
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    • v.8 no.1
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    • pp.89-100
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    • 2005
  • This study is to compare contents of mathematics textbooks of Korea and Russia laying stress on topic 'congruence of triangles'. We analyze and compare contents description system, relation between congruent conditions of triangles and construction problem, and jestification methods of congruent conditions of triangles in Korean and Russian mathematics textbooks.

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Teachers' Understanding about Triangle Congruence Conditions (삼각형의 합동조건에 대한 교사들의 이해와 개선 방안)

  • Rim, Haekyung
    • School Mathematics
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    • v.16 no.2
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    • pp.219-236
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    • 2014
  • We recognized that most teachers are having insufficient understanding or misunderstanding about congruent conditions of triangles. So the purpose of this study was to analyze teachers's understanding about congruent conditions of triangles and to find the causes of teachers's misunderstanding. Most teachers have been misunderstanding that triangle determining- conditions are only 3 ways(SSS, SAS, ASA). And they have wrong confidence that 2 sides and a non included angle(ASS) is not always able to make one triangle. This study found that these teachers's misconception was from the textbook using now. As the result of this study, we suggested 7 improvement ways about planning of curriculum, writing of textbook and teacher training course.

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Teaching Geometry Proof with focus on the Analysis (분석법을 중심으로 한 기하 증명 지도에 대한 연구)

  • Na, Gwi-Soo
    • Journal of Educational Research in Mathematics
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    • v.19 no.2
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    • pp.185-206
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    • 2009
  • In the study, I conducted the teaching experiment designed to instruct proof to four 7th grade students by utilizing the analysis method. As the results of this study I could identified that it is effective to teach and learn to find proof methods using the analysis. The results of the study showed that four 7th grade students succeeded in finding the proof methods by utilizing the analysis and representing the proof after 15 hours of the teaching experiment. In addition to the difficulties that students faced in learning proof utilizing the analysis were related to the search for the light conditions for triangles to be congruent, symbolic representation of the proof methods, reinterpretation of drawings given in the proof problems.

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