14.1-平面及其基本性质ppt课件.ppt

1、(二期课改),14.1.平面及其基本性质(双语） Planes and Their Basic Propenties,1,光滑的桌面、平静的湖面等都是我们熟悉的平面形象，数学中的平面概念是现实平面加以抽象的结果。Smooth desktop, calm lake plane image, we are familiar with the concept of mathematical plane is a real plane to be abstract.,平面没有大小、厚薄和宽窄，平面在空间是无限延伸的。Plane has no size, width, thickness and pla

2、ne in space is infinite extension,2,一.平面 的描述性定义:the descriptive definition of Plane,1.由现实生活中的具体实物的客观形象: By the objective image of the concrete physical objects in real life:,(桌面,水面,操场),抽象出-数学中的平面概念. (desktop, the surface of the water, playground.) Abstract the - plane concept in mathematics.,数学中的平面具

3、有与生活中的平面一样的“平”的特征,但两者又是不尽相同的,数学中的平面没有厚度,并在空间无限延伸; The plane no thickness of mathematics and in the infinite extension of space;,数学中的平面概念可与平几中直线的概念相类比.,New interpretation,3,二.数学中表示平面的一般方法: a general method said plane,大写的英文字母Uppercase letters -,平面M;平面N; Plane M; Plane N; .,小写的希腊字母Lowercase Greek lette

4、r -,平面;平面;平面;Plane alpha; Plane beta; Gamma plane; .,平面上表示三个(或三个以上)点的字母Plane said three (or more) points in the letter -,(如图所示) (as shown),-平面ABCD. Plane of the ABCD,4,三.数学中 平面直观图 的具体画法 : a specific plane pictorial diagram drawing,由于平面是向四周无限延伸的,在纸上只能画出它的一个部分,通常把它画成一个平行四边形. Painting it into a paralle

5、logram,水平放置的平面-内角为45的平行四边形;其中一组对边呈水平方向,另一组对边的边长等于其一半.,垂直放置的平面-内角为45的平行四边形;其中一组对边呈铅垂方向,另一组对边的边长等于其一半.,5,三.数学中 平面直观图 的具体画法 : a specific plane pictorial diagram drawing,两个相交的平面Two intersecting plane-一定要画出它们的相交直线,如果一个平面的一部分被另一个平面遮住,可把被遮部分画成虚线或者不画. Must draw their intersecting lines,6,观察并研究图中矩形的六个面的不同画法,

6、加深对直观平面画法的理解和把握. Observe and study the six-sided rectangular figure painting, deepen understanding and grasp of the visual plane painting.,1.请作出两个垂直放置的相交平面的直观图. Please make a visual map of the two vertically intersecting plane.,7,(作法简述) (Description of practice),(1).可先作出不同的两个垂直放置的平面的直观图. Can make in

7、tuitive view of the type of two vertically disposed plane.,(2).注意画出相交直线和用虚线表示被遮部分直线. Note that drawing intersecting lines and use dotted line is covering part of the straight line,8,四.空间点,线,平面之间的相应位置关系的 集合语言 表示法: The space point, line, plane of the corresponding position of the relationship between

8、assembly language notation:,点- 组成集合的基本元素;,线- 由基本元素点组成的集合.,面-由基本元素点组成的集合.,点与直线的位置关系：The positional relationship of the points with straight lines,点A在直线l上-记作 ：Point A on the line lrecorded as,点B不在直线l上-记作: Point B is not in line l recorded as,点A在直线l上 也常被叙述成 直线l经过点A . Point A on the straight line l are

9、often described in a straight line l passing point A,9,直线与平面的位置关系：The position relationship between straight line and plane,*当直线l上的所有点都在平面上时,可把直线l看作是平面的子集,称直线l在平面上,或平面经过直线l-记作: When all of the points on the straight line l in the plane alpha, can be regarded as a straight line l is a subset of the p

10、lane alpha, said straight line l in the plane alpha,*当直线l与平面只有一个公共点A时,称直线l与平面相交于点A-记作:When the line l with planealpha is only one common point A, said the line l and the plane alpha intersect at points A - recorded as,10,*当直线l与平面没有公共点时,称直线l与平面平行-记作: When there is no common point line l with plane al

11、pha, said line l parallel to the plane alpha - referred to as:,l= 或 l.,11,点与平面的位置关系：The position relationship between point and plane:,点A在平面上-记作 : Point A on the plane alpha - referred to as,点B不在平面上-记作 : Point B is not on the plane alpha - referred to as,点A在平面上 也常被叙述成 直平面经过点A . Point A on the plane

12、alpha is often described as a straight plane alpha passes through the point A,12,平面与平面的位置关系：The positional relationship of the plane and the plane,*当平面上所有的点都在平面上时,称平面与重合. When the plane on all points in the plane on alpha beta, said plane of alpha and beta,*当不同的两个平面和平面有公共点时,可将它们的公共点的集合记为l,称平面与平面相交于l

13、-记作:When two different plane have a common point alpha and beta, can put their public collection points for l -referred to as,13,*当两个平面和平面没有公共点时,称平面与平面平行-记作:* When there is no common point in the two planes alpha and flat-beta, called the plane alpha and parallel to the plane beta - referred to as:,

14、= 或.,14,点、线、面之间的位置关系的语言叙述具有多变性; Point, line, plane positional relationship between the language Designation variability,点、线、面之间的位置关系是利用集合符号表示的,但其读法仍然是用几何语言的; Point, line, the positional relationship between the surface is represented by the use of a collection of symbols, but the method is still rea

15、d with a geometric language;,结合图161矩形的点、线、面之间的位置关系,加深理解上述集合符号的表示法; Combined 16-1 the point of the rectangle, line, the positional relationship between the surface and deepen understanding of the representation of the collection of symbols,=l 实际表示一条直线,下节待学.,注意集合符号 与 的不同含义与不同的用途;,15,课本(P89)练习16.1: 1 ，2 .,请根据你在这节课所学的知识谈谈你的收获与体会. Based on the knowledge you have learned in this lesson to talk about your harvest and experience,*请同学自觉预习新课文*,16,一课一练(P36)16.1: 1 ,2 ,3 .,1.用集合符号表示下列几何语言所叙述的空间图形,并画图表示.,(1).直线l与平面相交于点A,直线AB在平面上;,(2).直线a与平