内容正文:
4.1.2 点、线、面、体
学习目标
1.通过从实物和具体模型的抽象,了解几何体、平面和曲面、直线和曲线、点等概念;
2.了解几何图形都是由点、线、面、体组成的,能正确判断由点、线、面经过运动变化形成的简单的几何图形;
3.通过点、线、面、体的变化过程,渗透转化、化归、变换的思想;
4.经历观察、思考、分析等过程,养成主动探索、求知的学习态度,激发学生对数学的好奇心和求知欲.
点
线
面
体
2
常见的几何体
1. 你知道这些几何体是由什么围成的吗?
2. 下图中的图形分别有哪些面?这些面有什么
不同吗?
以上立体图形都是几何体,简称体.
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3
图中有哪些你熟悉的立体图形?
球体
长方体
圆柱
正方体
4
线与线
相交成点
面与面相交成线,线有直线和曲线
体由面围成,面有平面和曲面
由点、线、面运动而形成的图形
这可以说成:点动成线.
笔尖可以看作是一个点,这个点在纸上运动时,形成了什么?
问题:
汽车雨刷可以看作什么几何图形?它在挡风玻璃上运动时的路线形成什么几何图形?
思考
7
线动成面
面动成体
课堂测试
1. 围成圆柱体的面有 ( )
A. 1个 B. 2个 C. 3个 D. 多于3个
2. 下列说法:①平面上的线都是直线;②曲面上
的线都是曲线;③两条线相交只能得到一个交
点;④两个面相交只能得到一条直线,不正确
的有 ( )
A. 4个 B. 3个 C. 2个 D. 1个
C
A
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10
课堂测试
3.请将下列的平面图形和将它如图绕虚线旋转
一周后得到的几何体连线.
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11
课堂测试
4.将一个直角三角形ABC绕它的一边旋转,旋转后所得的几何体可能是下面图中的哪个 .
(1)
(2)
(3)
(4)
(2)(3)(4)
解:以AC边所在的直线为轴,旋转一周所形成的图 (2)的圆锥体;
以BC边所在的直线为轴,旋转一周所形成的图(3)的圆锥体;
以AB边所在的直线为轴,旋转一周所形成的图(4)的几何体.
(5)
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12
几何图形
构成图形的基本元素
点
线
面
体
无大小
直线
曲线
无粗细
平面
曲面
无薄厚
物体的图形
交成
动成
动成
交成
动成
交成
课堂小结
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14
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