• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• The Mathematical Education
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• v.48 no.3
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• pp.287-302
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• 2009

This study investigated how 5th grade students found and understood triangle congruence conditions (SSS, SAS, ASA). In particular, this study focused on children's processes of discovering triangle congruence conditions and the obstacles which they encountered in the process of making sense of these conditions. Our data indicates that inquiring the cases in which less than three factors of triangle are given is helpful for children to guess triangle congruence conditions and understand the minimal characteristic of these conditions. And the degree of difficulty of discovering each congruence condition is different. Children discovered SAS condition and ASA condition easily, but it was hard for them to discover and understand that SSS was also a triangle congruence condition because they connected the length of a given side with the use of a scaled ruler not a compass.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.131-145
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• 2005

This study intends to analyze didactically on triangle-determining conditions and triangle-congruence conditions. The result of this study revealed the followings: Firstly, many pre-service mathematics teachers and secondary school students have insufficient understanding or misunderstanding on triangle-determining conditions and triangle-congruence conditions. Secondly, the term segment instead of edge may show well the concern of triangle-determining conditions. Thirdly, when students learn the method of finding six elements of triangle using the law of sines and cosines in high school, they should be given the opportunity to reflect the relation and the difference between triangle-determining situation and the situation of finding six elements of triangle. Fourthly, accepting some conditions like SSA-obtuse as a triangle-determining condition or not is not just a logical problem. It depends on the specific contexts investigating triangle-determining conditions. Fifthly, textbooks and classroom teaching need to guide students to discover triangle-deter-mining conditions in the process of inquiry from SSS, SSA, SAS, SAA, ASS, ASA, AAS, AAA to SSS, SAS, ASA, SAA. Sixthly, it is necessary to have students know the significance of 'correspondence' in congruence conditions. Finally, there are some problems of using the term 'correspondent' in describing triangle-congruence conditions.

• 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.

• 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.

• 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.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• 주택과사람들
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• no.11 s.28
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• pp.46-47
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• 1992

• Journal of the Korean Society of Propulsion Engineers
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• v.19 no.4
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• pp.102-109
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• 2015

The methodology to calculate loads on the bearings of the gas-turbine engine is presented for design of high-speed bearing. Firstly, the loads on the bearings are formulated according to the force and moment equilibrium with gyroscopic moment in three-dimensional space. Afterward, operating loading conditions of the engine are presented by applying the Joint Service Specification Guide, and magnitudes of transient and steady bearing loads are estimated based on the operating conditions. The calculated loading conditions of the bearings will be used for the essential design boundaries for the detail structural design and rig test.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.299-327
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• 2023

In this study, we tried to find out the level of inductive reasoning ability and the aspects of visualization components shown in students in the class using exploratory software for the 'congruence and symmetry' unit in the second semester of the 5th grade of elementary school. To this end, classes using GeoGebra, one of the exploratory software, were conducted for a total of 19 students in one class of fifth graders in elementary school, and the results of the students' activities were analyzed. As a result of this study, the level of inductive reasoning ability of students remained at a similar level or developed, and it was shown that students inferred new properties of shapes using various functions of software inductively. In addition, in terms of visualization, students were able to quickly and easily draw shapes that met the conditions, and unlike the paper-and-pencil environment, using the 'measurement' and 'symmetry' functions, they transformed and manipulated complex yet precisely congruent and symmetrical external representations. Based on these analysis results, implications for the use of exploratory software in the area of figures were derived.