高一数学必修第一章空间几何体上.ppt

及柱、锥、台、球的结构特征 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 问题1：观察下面的图片, 这些图片中的物体 具有怎样的形状?我们如何描述它们的形状? 如果我们只考虑物体的形状和大小，而不考 虑其它因素，那么由这些物体抽象出来的空 间图形就叫做空间几何体。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 思考6：一般地，怎样定义多面体？围 成多面体的各个多边形，相邻两个多边 形的公共边，以及这些公共边的公共顶 点分别叫什么名称？ 面 顶点 棱 由若干个平面 多边形围成的 几何体叫做多 面体 . Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 思考7：一般地，怎样定义旋转体？ 轴 由一个平面图形绕它所在平面内的 一条定直线旋转所形成的封闭几何体 叫做旋转体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 多面体 棱 柱 棱 锥 棱台 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 旋转体 圆柱 圆锥 圆台 球 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一、 观察下列几何体并思考：具备哪 些性质的几何体叫做棱柱? A B C D A1 A1 B1 B1 C1 C1 D1 AB C A1 B1 C1 D1 E1 A B C E D Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1、定义：有两个面互相平行，其余各面都 是四边形，并且每相邻两个四边形的公共边都 互相平行，由这些面所围成的几何体叫做棱柱 。 两个互相平行的平面叫做棱柱的底面，其 余各边叫做棱柱的侧面。 相邻侧面的公共边叫做棱柱的侧棱。 侧面与底的公共顶点叫做棱柱的顶点。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 底面 侧面 侧棱 顶点 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 有两个面互相平行， 其余各面都是平行四 边形的几何体是棱柱. 命题是否正确 ，为什么？ 思考： 定义：有两个面互相平行，其余各面都是四边 形，并且每相邻两个四边形的公共边都互相平 行，由这些面所围成的几何体叫做棱柱。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2、棱柱的分类：棱柱的底面可以是三 角形、四边形、五边形、 我们把这样 的棱柱分别叫做三棱柱、四棱柱、五棱柱、 三棱柱四棱柱五棱柱 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 3、棱柱的表示法(下图) 用平行的两底面多边形的字母表示棱 柱,如：棱柱ABCDE- A1B1C1D1E1 。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 课堂练习: 1. 下面的几何体中，哪些是棱柱？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 二、棱锥的结构特征 观察下列几何体,有什么相同点 ？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1 1、棱锥的概念、棱锥的概念 有一个面是多边形，其余各面是有 一个公共顶点的三角形， 由这些面所围 成的几何体叫做棱锥。 这个多边形面叫做棱锥的底面 。 有公共顶点的各个三角形叫 做棱锥的侧面。 各侧面的公共顶点叫做 棱锥的顶点。 相邻侧面的公共边叫做棱锥 的侧棱。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 棱锥的底面 棱锥的侧面 棱锥的顶点 棱锥的侧棱 S AB C D E Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 下列命题是否正确？ 有一个面是多边形，其余各面都是三角 形的立体图形一定是棱锥. 思考 明矾晶体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2、棱锥的分类： 按底面多边形的边数，可以分为三 棱锥、四棱锥、五棱锥、 A B C D S 3、棱锥的表示方法：用表示顶点和底面 的字母表示，如四棱锥S-ABCD。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 五、棱台的结构特征 B1 A1 C1 D1 C1 B1 A1 D1 棱锥：有一个面是多边形，其余各 面是有一个公共顶点的三角形，由这 些面所围成的几何体叫做棱锥。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1、棱台的概念：用一个平行于棱锥底面 的平面去截棱锥，底面和截面之间的部分 叫做棱台。 C1 B1 A1 D1 上底面 下底面 侧面 侧棱 顶点 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 2、由三棱锥、四棱锥、五棱锥截得 的棱台，分别叫做三棱台，四棱台， 五棱台 3、棱台的表示法： 棱台用表示上、下底面各顶点的字 母来表示，如右图，棱台ABCD-A1B1C1D1 。 C1 B1 A1 D1 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 判断:下列几何体是不是棱台,为什么? (1) (2) 辨析 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 棱柱、棱锥、棱台的结构特征比较 结结构特征棱柱棱锥锥棱台 定义义 底面 侧侧面 侧侧棱 平行于底面 的截面 过过不相邻邻 两 侧侧棱的截 面 两底面是全等的 多边形 平行四边形 平行且相等 与两底面是全等的 多边形 平行四边形 多边形 三角形 相交于顶点 与底面是相似的 多边形 三角形 两底面是相似的 多边形 梯形 延长线交于一点 与两底面是相似的 多边形 梯形 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 思考：既然棱柱、棱锥、棱台都 是多面体，那么它们之间有怎样 的关系？当底面发生变化时，它 们能否相互转化？ 棱台的上底面扩大 上下底面全等 棱台的上底面缩小 为一个点 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 旋转一周。 矩形直角三角形半圆直角梯形 圆柱圆锥球圆台 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 四、圆柱的结构特征 矩 形 O1 O 定义：以矩形的一边所在直线为旋转轴 ，其余三边旋转形成的曲面所围成的旋转 体叫做圆柱。 （4）无论旋转到什么位置,不垂 直于轴的边都叫做圆柱的母线。 （3）平行于轴的边旋转而 成的曲面 叫做圆柱的侧面。 （2） 垂直于轴的边旋转而 成的圆面叫做圆柱的底面。 （1）旋转轴叫做圆柱的轴。 A B A A O B O 轴 底面 侧 面 母 线 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 五、圆锥的结构特征 直角三角形 S AO （4）无论旋转到什么位置,不 垂直于轴的边都叫做圆锥的母 线。 （3）不垂直于轴的边旋转而成 的曲面叫做圆锥的侧面。 （2） 垂直于轴的边旋转而成的 圆面叫做圆锥的底面。 （1）旋转轴叫做圆锥的轴。 定义：以直角三角形的一条直角边所 在直线为旋转轴，其余两边旋转而成 的面所围成的旋转体叫做圆锥。 S 顶点 A B O 轴 侧 面 母 线 BEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 六、圆台的结构特征 定义：用一个平行于圆锥底面的平面去截 圆锥，底面与截面之间的部分，这样的几 何体叫做圆台。 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. O O 底面 底面 轴 侧面 母线 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1平行于圆柱，圆锥，圆台的 底面的截面是什么图形？ 过圆柱，圆锥，圆台的旋转 轴的截面是什么图形？ 性质1：平行于底面的截面都是圆。 性质2：过轴的截面（轴截面）分别是全等的矩 形，等腰三角形，等腰梯形。 想一想？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 七、球的结构特征 O 球心 半径 A B 球的定义：以半圆的直径所在直线为旋转轴， 半圆面旋转一周形成的旋转体叫做球体，简称 球。 （1）半圆的半径叫做球的半径。 （2）半圆的圆心叫做球心。 （3）半圆的直径叫做球的直径。 2、球的表示： 用表示球心的字 母表示，如球O Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 球 球面: 半圆弧旋转所成的曲面. 轴 其中半圆的圆心叫做球的球心，半 圆的半径叫做球的半径，半圆的直 径叫做球的直径。 用一个平面去截球体得到的截 面是什么图形？ 性质3：用一个平面去截球体得 到的截面是一个圆。 想一想？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 从平面到空间 例1如图，将直角梯形ABCD绕AB边所在的直线 旋转一周，由此形成的几何体是由哪些简单几何 体构成的？ A B CD Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 试一试、想一想 AB C D 如图，将平行四边形ABCD绕AB边所在的直线旋转一周， 由此形成的几何体是由哪些简单几何体构成的？ Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 1.1.2简单组合体 的结构特征 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 日常生活中我们常用到的日用品，比如：消毒液、 暖瓶、洗洁精等的主要几何结构特征是什么？ 简单组合体简单组合体 由柱、锥、台、球组成了一些简单的组合体认 识它们的结构特征要注意整体与部分的关系 圆柱 圆台 圆柱 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 走在街上会看到一些物体，它们的主要几何结构特 征是什么？ 简单组合体简单组合体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 一些螺母、带盖螺母又是有什么主要的几何结构特 征呢？ 简单组合体简单组合体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 蒙古大草原上遍布蒙古包，那么蒙古包的主要几何 结构特征是什么？ 简单组合体简单组合体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 居民的住宅又有什么主要几何结构特征？ 简单组合体简单组合体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile .Created with Aspose.Slides for .NET 3.5 Client Profile . Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd. 下图是著名的中央电视塔和天坛，你能说说它们的 主要几何结构特征吗？ 你能从旋转体的概念说说它们是由什么图形旋转而 成的吗？ 简单组合体简单组合体 Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Pro