相交线和平行线讲义

1、例题：图中1和2是对顶角的是 （ ） a b c deoadbfc例题：如图所示，三条直线相交于点o，说出图中的对顶角。odebca对顶角的性质：对顶角相等例题：如图所示，直线ab与cd相交于点o，oe是dob的平分线， 若aoc=76，则eob= 。coabd例题：如图所示：直线ab与cd相交于点o，已知boc=60，说出下列各个角的度数。eabodc例题：如图所示：直线ad与be相交于点o，doe与coe互余，coe=62，求aob的度数。理解两条直线互相垂直的有关概念aocdb若两直线与m先交构成的四个角中有一个角是直角，就说着两条直线互相垂直，记作：，直线称为垂线，交点就是垂足。例题：

2、如图所示：oaob，ocod，若aod=144，则boc= 。1、如图1所示,三条直线ab,cd,ef相交于一点o,则aoe+dob+cof等于( )a.150 b.180 c.210 d.120 (1) (2) (3)2、下列说法正确的有( ) 对顶角相等;相等的角是对顶角;若两个角不相等,则这两个角一定不是对顶角;若两个角不是对顶角,则这两个角不相等. a.1个 b.2个 c.3个 d.4个 3、如图2所示,直线ab和cd相交于点o,若aod与boc的和为236,则aoc的度数为( ) a.62 b.118 c.72 d.594、如图3所示,直线l1,l2,l3相交于一点,则下列答案中,全

3、对的一组是( ) a.1=90,2=30,3=4=60; b.1=3=90,2=4=30 c.1=3=90,2=4=60; d.1=3=90,2=60,4=305、如图，则（ ） a b c d 6、若ab，cd则a与c的关系是（ ）a平行 b垂直 c相交 d以上都不对7、 体育课上，老师测量跳远成绩的依据是（ ）.（a）平行线间的距离相等 （b）两点之间，线段最短（c）垂线段最短 （d）两点确定一条直线二、填空题1、如图4所示,ab与cd相交所成的四个角中,1的邻补角是_,1的对顶角_.（6）（5）（4） 2、如图4所示,若1=25,则2=_,3=_,4=_.3、如图5所示,直线ab,cd,

4、ef相交于点o,则aod的对顶角是_,aoc的邻补角是_;若aoc=50,则bod=_,cob=_.4、a、b、c是直线，且ab，bc，则a与c的位置关系是_4、如图6所示,已知直线ab,cd相交于o,oa平分eoc,eoc=70,则bod=_.5、对顶角的性质是_.6、如图7所示,直线ab,cd相交于点o,若1-2=70,则bod=_,2=_. (7) (8) (9)7、如图8所示,直线ab,cd相交于点o,oe平分aoc,若aod-dob=50,则eob=_.8、如图9所示,直线ab,cd相交于点o,已知aoc=70,oe把bod分成两部分,且boe:eod=2:3,则eod=_.9、如图

5、，直线a、b被c所截，al于m，bl于n，1=66，则2=_10、如图，acb=90，cdab，则图中与a互余的角有 个，它们分别是 a= ，根据是 判断：1、 一条直线有无数条平行线。 （ ）2、 过直线外一点可以作无数条直线与已知直线平行。 （ ）3、 过任意一点可作已知直线的一条平行线。 （ ）作图题 图5-22 图5-211、如图5-21，过p点，画出oa、ob的垂线如图5-22，过p点，画出ab、cd的垂线和平行线 2、如图5-23，是一条河，c河边ab外一点： （1）过点c要修一条与河平行的绿化带，请作出正确的示意图 （2）现欲用水管从河边ab，将水引到c处，请在图上测量并计算出水

6、管至少要多少?（本图比例尺为1：2000）如图所示,ab,cd,ef交于点o,1=20,boc=80,求2的度数. 如图所示,l1,l2,l3交于点o,1=2,3:1=8:1,求4的度数.提高训练:如图所示,ab,cd相交于点o,oe平分aod,aoc=120,求bod,aoe的度数.如图所示,直线a,b,c两两相交,1=23,2=65,求4的度数.探索发现已知点o是直线ab上一点,oc,od是两条射线,且aoc=bod,则aoc与bod是对顶角吗?为什么?能力提高如图16所示,直线ab,cd相交于o,若1=40,则2的度数为_如右上图是一个的正方形，现要在中轴线上找一点，使最小，则的位置应选

7、在（ ）点处 apbqcrds3035如图所示，已知直线相交于，且，求的度数如图，efad，1 =2，bac = 70。将求agd的过程填写完整。efad，（） 2 = 。（）又 1 = 2，（） 1 = 3。（） ab 。（）bac + = 180。（）又bac = 70，（）agd = 。（）待添加的隐藏文字内容3abcda11b11c11d11在长方体abcd-efgh中，（1）与棱ab平行的棱有哪些？（2） 与棱ad平行的棱有哪些？（3） （3）连结ac、eg，ac、eg是否平行？在同一平面内，一个角的两边与另一个角的两边分别平行，那么这两个角的大小关系是 。读下列语句作图并解答（1）

8、 任意作一个aob；（2） 在角内部取一点p；（3） 过电p分别作pqoa，pmob。若aob=30，猜想mpq是多少度？课后作业： （第1题） （第3题）1、如图1,acbc,cdab, 垂足为d,图中共有_个直角,它们是_,图中线段_的长表示点c到ab的距离，线段_的长表示点a到bc的距离.2、如图，一个零件abcd需要ab边与cd边平行，现只有一个量角器，测得拐角abc=120，bcd=60这个零件合格吗？_填（“合格”或“不合格”）3、 如图所示,直线ab与cd相交于点o,aoc:aod=2:3,求bod的度数. （第2题）4、若4条不同的直线相交于一点,则图中共有几对对顶角?若n条不

9、同的直线相交于一点呢?5、在一个平面内任意画出6条直线,最多可以把平面分成几个部分?n条直线呢?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 sid

10、es 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

11、 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

12、 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 a

13、nniversary 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

14、 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. i

15、n 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 -

16、 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 kilomete

17、rs), 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 w

18、ould 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 repeat

19、ed 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