由教学“角平分线定理的逆定理”引发的问题探究

• 作 者: 郑建斌
• 机 构: 浙江省台州市椒江区第五中学,
• 出 处: 中小学数学(初中版)
• 发表日期: 2004年期
• 关键词: 角平分线 问题解决 辅助线 人教版 对角点 思考角度 已知点 全班交流 APEO 记忆性

对“角平分线定理的逆定理”(人教版数学八年级上册第50页)的教学,笔者是这样设计的:首先,让学生用几何语言描述上节课的角平分线定理.然后,让学生通过操作、归纳、猜想、证明得出角平分线定理的逆定理.接着,我让学生比较这两个定理的区别与联系,即这两个定理都有三个量:①∠1=∠2;②PD上OA,PE⊥OB;③PD=PE(如图1).角平分线定理是由①、②

For the teaching of “Inverse Theorem of the Angle Bisection Theorem” (PEP. Grade 8, p. 50), the author designed it this way: First, let the students describe the angle bisector theorem of the class in geometric language. Then, let the student derive the inverse theorem of the angle bisector theorem by manipulating, inducing, guessing, proofing, and then letting students compare the differences and connections between the two theorems, that is, both theorems have three quantities: = ∠2; ② PD on the OA, PE ⊥ OB; ③ PD = PE (Figure 1). Angle bisector theorem is ①, ②