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1、精品_精品资料_可编辑资料 - - - 欢迎下载精品_精品资料_高二数学学问点总结大全 必修第 1 章空间几何体 12 圆柱的表面积S2 rl3 圆锥的表面积 Srl4 圆台的表面积 Srl2 r 2r 2r 2RlR2可编辑资料 - - - 欢迎下载精品_精品资料_可编辑资料 - - - 欢迎下载精品_精品资料_1 .1柱、锥、台、球的结构特点5 球的表面积 S4 R2可编辑资料 - - - 欢迎下载精品_精品资料_1. 2空间几何体的三视图和直观图（二）空间几何体的体积可编辑资料 - - - 欢迎下载精品_精品资料_11 三视图：正视图：从前往后侧视图：从左往右 俯视图：从上往下 22 画
2、三视图的原就：1 柱体的体积2 锥体的体积3 台体的体积VS底 h底V1 Sh 3VS1（ 上3S上 S下S下 h可编辑资料 - - - 欢迎下载精品_精品资料_长对齐、高对齐、宽相等4 球体的体积V4R33其次章 直线与平面的位置关系可编辑资料 - - - 欢迎下载精品_精品资料_可编辑资料 - - - 欢迎下载精品_精品资料_33 直观图：斜二测画法44 斜二测画法的步骤：（1）. 平行于坐标轴的线依旧平行于坐标轴.（2）. 平行于 y 轴的线长度变半,平行于 x, z 轴的线长度不变.（3）. 画法要写好.5 用斜二测画法画出长方体的步骤： （1）画轴（ 2）画底面（ 3）画侧棱（ 4）
3、成图1.3空间几何体的表面积与体积（一 ）空间几何体的表面积1 棱柱、棱锥的表面积：各个面面积之和2.1 空间点、直线、平面之间的位置关系2.1.11 平面含义：平面是无限延展的2 平面的画法及表示（1） 平面的画法：水平放置的平面通常画成0一个平行四边形,锐角画成45 ,且横边画成DC邻边的 2 倍长（如图）（2） 平面通常用希腊字母 、 等表示, AB如平面、平面等,也可以用表示平面的平行四边形的四个顶点或者相对的两个顶点的大写字母来表示,如平面AC、平面 ABCD等.3 三个公理：可编辑资料 - - - 欢迎下载精品_精品资料_proved t hat a pe opl e and a
4、nati on, if it doe s not have its own spirit ual pillar, t here is no unity of spirit ual support, it m eans that no soul , will l ose cohesi on and vitalit y. Fig uratively speak ing, a sack of potatoes, qua ntity cannot be too a team, form a joi nt force ; only like granite, so closely United t o
5、form invincibl e, no difficult means of strength. Nati onal rejuvenation of Chi nese dream, not only embodi es the common intere sts and pursuits, and covers a variety of groups and classe s, ha s a wi de applicability a nd i ncl usive, with a strong i nt egrating force a nd lead t he force. She em
6、bodies the aspirations of several generati ons of Chi nese, reflecti ng today . Into sex a nd purit y, and the i nevita ble requirement of constantly impr oving t he partys g overni ng ca pacit y. Strengt heni ng the construction of the a dvanced nature and purit y, the cor e problem is a lways main
7、tai ning t he partys flesh -and-blood tie s with t he masse s, so that our party will always be the most w hol ehearte d support of the ma sses. Must take the fundamental i nterests of the overw helming majority of the pe ople as the party all the starting poi nt and ending poi nt, the party ha s al
8、ways been a common fate with the masses, t his is the magi c weapon for our party to alway s maintain t he adva nce d nat ure a nd purity. Strengthe ning t he constructi on of partys a dvanced nature a nd purity a nd e nha nci ng the partys rul ing a bility will ev entual ly be im plemented to reali
9、ze , safeguar d and devel op t he funda mental interests of the over whelmi ng majority of the pe opl e. All the work merits t his i s a measure of the partys fundamental standards, is a measure of the partys a dvanced nature a nd purity sta ndar ds. Believe who, de pendi ng on who, who, sta ndi ng
10、on the position of the overwhelming major ity of the pe ople are always, always realize , safeguar d and dev el op t he fundame ntal interests of the overw helming majority of the pe ople , it is a touchstone of the Marxist party of judgeme nt, is also sign of Marxist party is different from other p
11、olitical parties. Marxist politi cal party ha s a clear politi cal position and hist orical mission: for the i nterests of the vast majority of peopl e, committed to the fundamental i nterests of the overwhelming majority of the pe ople. From the day of the e stablishment of the Chi nese Communist P
12、art y, always a dhere to basi c princi ples of hi storica l materialism, for the interest s of the most people as t heir goal, alway s servi ng as its fundamental purpose a nd values. Fully trust the masses, cl osely rely on the masses mai ntain flesh-a nd-bl ood ties with t he masse s is always the
13、 source of our party full of vigor and vitalit y, is always t he most determined i n the development of our party and our countr y. Conscienti ously accept supervi sion by the masses, pay attenti on t o listen to t he masse s assessment, w hich itself was the partys adva nce d nat ure and purity i n
14、to pra ctical a ction to realize the fundamental interest s of the over whelmi ng majority of the people. At present, the party committees a nd lea ding cadres a nd t he Governme nt generally value the close relations with t he masse s, do a l ot of productive work, but there are still some可编辑资料 - -
15、 - 欢迎下载精品_精品资料_可编辑资料 - - - 欢迎下载精品_精品资料_（1） ）公理 1：假如一条直线上的两点在一个平面内, 那么这条直线在此平面内符号表示为ALBL= L AALB公理 1 作用：判定直线是否在平面内（2） ）公理 2：过不在一条直线上的三点,有且只有一个平面. A3 等角定理：空间中假如两个角的两边分别对应平行,那么这两个角相等或互补4 留意点： a 与 b 所成的角的大小只由 a、b 的相互位置来确定,与O 的挑选无关,为了简便,点 O 一般取在两直线中的一条上.2 两条异面直线所成的角 0 , . 当两条异面直线所成的角是直角时,我们就说这两条异面直线相互垂直,
16、记作 a b.B 两条直线相互垂直,有共面垂直与异面垂直两种情形.可编辑资料 - - - 欢迎下载精品_精品资料_符号表示为： A、B、C三点不共线 = 有且只有一个平面 ,C使 A、B 、C .公理 2 作用：确定一个平面的依据.（3） ）公理 3：假如两个不重合的平面有一个公共点, 那么它们有且只 运算中,通常把两条异面直线所成的角转化为两条相交直线所成的角.2.1.3 2.1.4空间中直线与平面、平面与平面之间的位置关系1、直线与平面有三种位置关系：可编辑资料 - - - 欢迎下载精品_精品资料_有一条过该点的公共直线.符号表示为： P = =L,且 PL公理 3 作用：判定两个平面是否
17、相交的依据2.1.2空间中直线与直线之间的位置关系1 空间的两条直线有如下三种关系：PL（1） 直线在平面内 有很多个公共点（2） 直线与平面相交 有且只有一个公共点（3） 直线在平面平行 没有公共点指出：直线与平面相交或平行的情形统称为直线在平面外,可用a 来表示可编辑资料 - - - 欢迎下载精品_精品资料_共面直线相交直线：同一平面内,有且只有一个公共点. 平行直线：同一平面内,没有公共点.可编辑资料 - - - 欢迎下载精品_精品资料_异面直线：不同在任何一个平面内,没有公共点.2 公理 4：平行于同一条直线的两条直线相互平行.符号表示为：设 a、b、c 是三条直线aa=Aa可编辑资料
18、 - - - 欢迎下载精品_精品资料_a bcb=a c2.2. 直线、平面平行的判定及其性质可编辑资料 - - - 欢迎下载精品_精品资料_强调：公理 4 实质上是说平行具有传递性,在平面、空间这个性质都适用.公理 4 作用：判定空间两条直线平行的依据.2.2.1 直线与平面平行的判定1、直线与平面平行的判定定理：平面外一条直线与此平面内的一条直可编辑资料 - - - 欢迎下载精品_精品资料_proved that a people a nd a nati on, if it does not have its own spiritual pilla r, there i s no unit
19、y of spiritual support, it m eans that no soul, will lose cohesion a nd vitalit y. Figuratively speaki ng, a sa ck of potat oes, quantity cannot be too a team, form a joi nt force; only like granite, so closely United t o form invincible , no difficult means of strength. National rejuvenati on of Ch
20、ine se dream, not only embodie s the common i nterests and pursuit s, and covers a variety of groups and cla sses, has a wi de a ppli cability a nd i ncl usive, wit h a strong integrating force a nd lea d the force. She em bodies the aspi rations of several ge nerations of Chine se, reflecti ng toda
21、y . Into sex and purit y, and the i nevitable re quireme nt of constantly im proving the partys gover ning capa city. Stre ngthe ning the construction of the adva nce d nat ure and purit y, the core probl em is always maintai ning the partys flesh-a nd-blood tie s with the masses, so t hat our party
22、 will always be the most wholehearte d support of the masses.Must take the fundamental i nterests of the overwhelming majority of the people a s the party all the starting point a nd e ndi ng point, the party has alway s bee n a common fate with the masses, thi s is the magi c weapon for our party t
23、o alway s maintain the advanced nature a nd purity. Strengthe ning t he constr uction of partys a dvanced nature and purity and enhancing the partys ruli ng ability will event ually be im plemente d to realize, safeguard a nd develop the fundame ntal inte rests of the overw helming majority of the p
24、e opl e. All the w ork merits this i s a measure of the partys fundame ntal standards, is a measur e of the partys a dvanced nature and purity standards. Beli eve who, de pending on w ho, w ho, sta ndi ng on the positi on of the overw helming majority of the pe ople are always, alway s realize, safe
25、g uard a nd develop the fundame ntal interests of the overw helming majority of the pe ople , it is a touchstone of the Marxist party of judgeme nt, is also sign of Marxist party is different from other political parties. Marxist politi cal party ha s a clear politi cal position and hist orical miss
26、ion: for the i nterests of the vast majority of peopl e, committed to the fundamental i nterests of the overwhelming majority of the pe ople. From the day of the e stablishment of the Chi nese Communist Part y, always a dhere to basi c pri nciples of hi storica l materialism, for the interest s of t
27、he most people as t heir goal, alway s servi ng as its fundamental p urpose a nd values. Fully trust the masses, cl osely rely on the masses mai ntain flesh-a nd-bl ood ties with t he masse s is always the source of our party full of vigor and vitalit y, is always t he most determined i n the develo
28、pment of our party and our countr y. Conscienti ously accept supervi sion by the masses, pay attenti on t o listen to t he masse s assessment, w hich itself was the partys adva nce d nat ure and purity i nto pra ctical a ction to realize the fundamental interest s of the over whelmi ng majority of t
29、he people. At present, the party committees a nd lea ding cadres a nd t he Governme nt generally value the close relations with t he masse s, do a l ot of productive work, but there are still some可编辑资料 - - - 欢迎下载精品_精品资料_线平行,就该直线与此平面平行.简记为：线线平行,就线面平行.符号表示：a b = aab2.2.2 平面与平面平行的判定1、两个平面平行的判定定理：一个平面内的
30、两条交直线与另一个平面平行,就这两个平面平行.2、定理：假如两个平面同时与第三个平面相交,那么它们的交线平行.符号表示：= aab = b作用：可以由平面与平面平行得出直线与直线平行2.3 直线、平面垂直的判定及其性质可编辑资料 - - - 欢迎下载精品_精品资料_可编辑资料 - - - 欢迎下载精品_精品资料_2、判定两平面平行的方法有三种：（1） ）用定义.（2） ）判定定理.符号表示：a b a b = Pa b 2.3.1 直线与平面垂直的判定1、定义假如直线 L 与平面内的任意一条直线都垂直, 我们就说直线 L 与平面相互垂直,记作 L,直线 L 叫做平面 的垂线,平面 叫做直线 L
31、 的垂面.如图,直线与平面垂直时 , 它们唯独公共点 P叫做垂足.L可编辑资料 - - - 欢迎下载精品_精品资料_（3） ）垂直于同一条直线的两个平面平行.p2.2.3 2.2.4直线与平面、平面与平面平行的性质1、定理：一条直线与一个平面平行,就过这条直线的任一平面与此平面的交线与该直线平行.可编辑资料 - - - 欢迎下载精品_精品资料_简记为：线面平行就线线平行.符号表示：aaab= b作用：利用该定理可解决直线间的平行问题.2、判定定理：一条直线与一个平面内的两条相交直线都垂直,就该直线与此平面垂直.留意点： a 定理中的“两条相交直线”这一条件不行忽视.b 定理表达了“直线与平面垂
32、直”与“直线与直线垂直” 相互转化的数学思想.2.3.2 平面与平面垂直的判定可编辑资料 - - - 欢迎下载精品_精品资料_Accor ding to Office Party of mass li ne educati on practice activities le d group of unified arra ngements, units mai n led to for cadres workers Shang a times party lecture , due to himself level limited, only put this stage conce ntra
33、ted learni ng of experie nce today a nd every one common with lear ning e xchange, pur pose is let we furt her de ep understanding mass li ne of connotati on, insiste d party of mass li ne, do masse s work, foll owi ng main from four a aspect s told: a, and full aware ness party of mass line education pra ctice a ctivities of major meaning Partys 18 major disti nct pr opose d to focus on the partys adva nce d nat ure and purity, in t