高二数学棱锥的念概和性质.pptx
14页
1.棱锥的概念2.棱锥的性质3.正棱锥直观图的画法4.多面体和正多面体Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date1Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date2(1)有一个面是多边形有一个面是多边形，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．棱锥是由这样一些面围成的几何体:(2)其余各面是有一个公共顶点的三角形(1)棱锥的定义:1.棱锥的概念Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date3（1）棱锥的底面棱锥的侧面（2）棱锥的棱棱锥的侧棱（3）棱锥的顶点, 底面的顶点（4）棱锥的高(3)棱锥的表示方法(2)棱锥的有关概念:---棱锥的底面---棱锥的侧面---棱锥的侧棱---棱锥的顶点棱锥的高-----Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date4棱锥的底面棱锥的侧面棱锥的顶点棱锥的侧棱棱锥的高SABCD EO棱锥的基本概念棱锥的基本概念Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date5(4)棱锥的分类分类标准2：正棱锥分类标准1：底面多边形的边数三棱锥、四棱锥、五棱锥……非正棱锥Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date6棱锥的分类分类标准：底面多边形的边数三棱锥四棱锥五棱锥六棱锥Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date7正棱锥正棱锥: :如果一个棱锥的底面是正多边形，并且顶点在底面 内的射影是底面的中心，这样的棱锥叫做正棱锥． 侧面等腰三角形底边上的高相等,它们叫做正棱锥的斜高．（1）各侧棱相等,各侧面都是全等的等腰三角形. （2）棱锥的高、斜高、斜高在底面内的射影组成一个直角三角形；棱锥的高、侧棱、侧棱在底面内的射影也组成一个直角三角形.正棱锥的性质:2.棱锥的性质Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date8正棱锥的性质正棱锥的性质1．各侧棱相等，各侧面都是 全等的等腰三角形．2．棱锥的高、斜高和斜高在 底面内的射影组成一个直角三角形 ；棱锥的高、侧棱和侧棱在底面内的 射影也组成一个直角三角形．Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date9这些等腰三角形底边上的高叫做正棱锥的 斜高,它们长度都相等．（1）各侧棱相等,各侧面都是全等的等腰三角形.（2）棱锥的高、 斜高、斜高在底面 内的射影组成一个 直角三角形；棱锥 的高、侧棱、侧棱 在底面内的射影也 组成一个直角三角 形。
GSACDEBOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOSBGOEvaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date10hh’Rra 2正棱锥中的基本图形正棱锥中的基本图形Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date11定理: 如果棱锥被平行于底面的平面所截， 那么截面和底面相似，并且它们面积的比等 于截得的棱锥的高和已知棱锥的高的平方比 ．一般棱锥的性质一般棱锥的性质Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date12定理：如果棱锥被平行于底面的平面所截，那么截 面和底面相似，并且它们面积的比等于截得的棱锥的 高与已知棱锥的高的平方比。
HSABCDEA’B’C’D’E’ H’已知：在棱锥S – AC中，SH是高 ，截面A’B’C’D’E’平行于底面， 并且与SH交于H’求证：截面A’B’C’D’E’∽底面 ABCDE，并且∴SA’B’C’D’E’ SABCDE=SH’2 SH2一般棱锥的性质一般棱锥的性质Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date13HSABCDEA’B’C’D’E’ H’证明：因为截面平行于底面，所以A’B’//AB，B’C’//BC ，C’D’//CD，…… ∴∠A’B’C’=∠ABC，∠B’C’D’=∠BCD …… 又因为过SA、SH的平面与截面和底面分别交于 A’H’和AH∴A’H’//AH由此得A’B’ AB=SA’ SA=SH’ SH 同理B’C’ BC=SH’ SH…∴A’B’ AB=B’C’ BC=SH’ SH…=因此截面A’B’C’D’E’∽底面ABCDE∴SA’B’C’D’E’ SABCDE=A’B’2 AB2=SH’2 SH2Evaluation only.Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd.Copyright 2004-2011 Aspose Pty Ltd.Date14例1、如图，已知正三棱锥S – ABC的高SO=h，斜高 SM=l，求经过SO的中点且平行于截面△A’B’C’的面 积。
SABCOA’B’C’ O’M解：连结OM、OA在Rt△SOM中， OM= √l 2 - h 2 因为棱锥S – ABC是正棱锥 所以点O是正三角形ABC的中心√AB=2AM=2•OM •t a n 600 =2√3 •l 2 - h 2S△ABC=AB2=×4×3（ l 2 - h 2）根据棱锥截面的性质，有 S △A’B’C’ S△ABC=S △A’B’C’=（l 2 - h 2）过高的中点且平行于底面的截面叫做中截面Evaluation only.Evaluation only. Created wit。
