The Study of Similarity and Congruence Properties of Triangles from Parallel Postulate

• Main Authors: Ming-Hui Cheng, 鄭銘惠
• Other Authors: Mu-Ming Wong
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/6em7u8

碩士 === 中原大學 === 應用數學研究所 === 106 === The main purpose of my study is to discuss the equivalence of triangular congruent, parallel lines, proportional line segments, and triangular similarities. By deconstructing and rebuilding textbooks, I will reorganize another set of systematic knowledge. My research starts with parallel postulate of Euclid''s Elements and uses four lemmas: parallel lines are always the same equidistant, if the distance between two straight lines is the same, lines will be parallel, the parallel cuts two sides of triangle into proportional line segments, and converse theorem, to explore the equivalence of the similarities and congruence properties of triangles. Through my study, students will focus on the key role of certain theorem in the development of math, link the past experience, and then understand the entire math structure. And interpret more advanced math knowledge. Then finally make math conceptual connections. The results are as follows： First, by exploring the geometric proof, we can strengthen students'' understanding of math theorems and develop their ability to think in multiple ways. Second, with the guiding of math history, students can learn actively to explore the roots of the concept and understand the beauty of math. Third, math is a language, the most perfect training and thinking tool, and students can understand deeply after proficiency.