一道几何题的多种解法

• 作 者: 陈海锋
• 机 构: 江苏省南通市如东县茗海中学,
• 出 处: 理科考试研究
• 发表日期: 2012年02期
• 关键词: 几何题 学生 思考题 题目 解法 方法

自习课上,学生拿着这样的一道题来问我怎么做:题目已知:AB∥CD,AE、DE分别平分∠BAD和∠ADC,BC过点E,求证:AD=AB+CD.细细看过之后,觉得这道题的做法还挺多,索性就将它作为了一道思考题,留着第二天上课时,与学生一道探讨.第二天上肯时,发现同学们探讨出的方法还挺多,现将各种解法总结如下.一、利用角平分线的性质来解证法1如图2,过E作EF上AD,EG上CD,EH上AB,垂足分别是F、G、H.

Self-study class, the students took such a question to ask me how to do: subject known: AB ∥ CD, AE, DE respectively ∠ BAD and ∠ ADC, BC too E, verify: AD = AB + CD. After looking carefully, think this problem quite a lot of practice, simply think of it as a question of thinking, leaving the next day class, and students together to explore the next day when willing to find the students to explore The method is quite a lot, is now summarized in various solutions are as follows: First, the use of the nature of bisecting lines to prove the law 1 As shown in Figure 2, E over EF on AD, EG on CD, EH on AB, F, G, H.