國中數學幾何比例之解題策略

比例性質在幾何證明中有舉足輕重的地位，在國中幾何範圍就涵蓋了平面幾何圖型、平行四邊形、梯形、相似形、圓、三心等單元。本研究目的在於幫助國中生遇到與比例性質相關的幾何證明問題時，可能遇到的困難；另外又該如何思考與解決問題？而教師如何引導學生，帶領學生從回想國中學過哪些幾何觀念與方法，從看懂題目與找到題目或圖形所提供的線索，到運用線索與過去經驗來逐步解決問題。最後再將常用的觀念與特殊技巧整理起來，成為類似題型的解題技巧。由於比例性質涵蓋範圍甚廣，此研究學生以平行性質、比例線段性質、相似性質為主要分類，其他延伸圖形的性質為輔助，而圓的相關性質並不討論。關鍵字：幾何比例、平行性質、比例線段性質、相似性質。

關鍵字

幾何比例；平行性質；比例線段性質；相似性質

並列摘要

Proportionality, which plays a very important role in geometric proof, contains plane geometry, parallelogram, trapezoid, similar figure, circle, and circumcenter, incenter, and centroid of a triangle in geometric range of junior high mathematics. The purpose of the study is to help junior high school students to solve the problems when dealing with the geometric proof questions relating to proportionality. In addition, it shows how teachers guide students, lead students to deal with the problems progressively by reviewing the concepts about geometry that they’ve learned in junior high school, comprehending the meaning of the questions, and using the clues from the text and the related experience learned before to solve the problems. Finally, students will know how to integrate what they’ve learned and applied the skills to other similar problems. Since the range of the proportionality is wide, the study mainly focuses on the classifications of parallel property, proportional segment property, and similarity. Other extend graphics are the secondary. And the relevant property of circle won’t be discussed here. Keywords：geometric proportion , parallel , proportional segment , similarity