立体几何垂直讲义.doc

专业好文档立体几何垂直讲义 一条直线与一个平面内的两条相交直线垂直，则该直线与此平面垂直.一个平面过另一个平面的垂线，则两个平面垂直.垂直于同一个平面的两条直线平行.两个平面垂直，则一个平面内垂直于交线的直线与另一个平面垂直.1.线面垂直的判定定理：一条直线与一个平面内的两条相交直线都垂直，则该直线与此平面垂直.afpdcb方法一 正方形（菱形）的对角线互相垂直. 1如图，已知四棱锥的底面是菱形, 平面, 点为的中点. 求证:平面.方法二:等腰三角形（等边三角形）三线合一（第18题图）2（本小题满分12分）如图，四棱锥pabcd的底面是菱形，papb，abc=60，点e为棱ab的中点求证：ab平面pce；3 如图所示，四棱锥的底面是边长为1的菱形，e是cd的中点，pa底面abcd，。（i）证明：平面pbe平面pab；abcdp方法三: 勾股定理4如图，在四棱锥中，底面是矩形已知， （）证明平面；5如图,在直三棱柱中, , , , , 点是的中点. (1)求证:;(2)求证:平面.6、如图5所示，四棱锥p-abcd的底面abcd是半径为r的圆的内接四边形，其中bd是圆的直径，。（1）求线段pd的长；（2）若，求三棱锥p-abc的体积。.面面垂直的判定定理：一个平面过另一个平面的一条垂线，则这两个平面垂直.7如图，在四面体abcd 中，cb= cd, adbd，点e 、f分别是ab、bd 的中点，求证：（）平面efc平面bcd (面面垂直的性质定理)8 如图，在四棱锥p-abcd中，侧面pad底面abcd,侧棱pa=pd=，底面abcd为直角梯形，其中bcad,abad,ad=2ab=2bc=2,o为ad中点。（1）求证：po平面abcd;9（本小题满分14分）已知s-abc中，平面sac平面sbcsa面abc，求证： bcac winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis are a lot less