角平分线习题的变式探究

• 作 者: 曹松峰
• 机 构: 河南焦作市教育局教研室,
• 出 处: 中学生数理化(八年级数学)(配合人教社教材)
• 发表日期: 2015年Z2期
• 关键词: 角平分线 变式 知识的掌握 《数学》 人教版 已知条件 数量关系 三等分 分角 面积法

角平分线的性质与判定是平面几何的核心内容之一.对课本中相关习题的变式探究,有助于对角平分线知识的掌握和理解.原题1(人教版《数学》(八年级上册)第17页第9题)如图1,∠1=∠2,∠3、∠4,∠A=100°.求x的值.解析:运用角平分线的定义和三角形内角和定理,易得x°=180°-∠2-∠4=180°-1/2(∠ABC+∠ACB)=180°-1/2(180°-100°)=140°.

The nature and judgment of the angle bisector is one of the core contents of plane geometry.Changes in the textbook related exercises help to grasp and understand the diagonal bisector knowledge.Proposal 1 (PEP Edition “Mathematics” ( Grade eight) page 17, No. 9) as shown in Figure 1, ∠1 = ∠2, ∠3, ∠4, ∠A = 100 °. Find the value of x. Resolution: The definition of angle bisector and the angle of the triangle The theorem is that x = 180 ° -∠2-∠4 = 180 ° -1/2 (∠ABC + ∠ACB) = 180 ° -1/2 (180 ° -100 °) = 140 °.