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课程简介

之前我们学过全等三角形,既要形状一致,又要大小相同。现在条件放松了,只要求形状一致,大小呢,就随意吧。这样就有了相似三角形。大家千万可别小看相似三角形,它可是三角形中难度最大的一节,除了涉及到角度相等的证明,还会涉及到探究边长的比例关系,而且题型还会更加的灵活多变。超级课堂从相似的起源讲起,也就是平行线分线段成比例探究相似存在的边长比例,历经相似判定的三大定理的学习,再献上各种相似应用的难题,在黄金分割比例的华美番外篇中顺利讲解整章内容。讲练结合,层层深入,超级课堂的粉丝们,值得典藏哦!

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视频列表
  • 1、如果全长线段和较长分线段的比值,恰好等于较长分线段和较短分线段的比值。那么我们就管这种比例叫做黄金比例,这个节点就是黄金分割点
    2、 黄金比用列方程的思想来解决
    3、 黄金比有两种说法,$1:0.618$或者$1.618:1$,总之都是长的比短的
    4、 黄金分割其实跟金条,money都没关系,而是在一条线段上完成的一种具有比例关系的分节
  • 1、黄金比的美来源于数学,深潜于人类的意识中,是最纯正和理想的
    2、 用尺规作图法画出一条线段的黄金分割点
  • 1、当看到一组平行线,然后有至少两条线穿过它们时,就要想到平行线等分线段定理啦
    2、 记住两条直线穿过五线谱的模型。如果这组平行线能等分一条直线,那就也能等分其他直线。
    3、 定理的两种应用,一是在梯形里,一是在三角形里。主要用来证明线段相等的关系
    4、 当条件或者问题中的线段关系集中在某一条边上时,你就要向这条边引一条平行的辅助线
  • 1、平行线等分线段定理,三条平行线截两条线段,所得线段对应成比例
    2、 要注意的是“对应成比例”,就是同一个平行线的空当,左右对应,左边是哪一段比哪一段,右边也是哪一段比哪一段
    3、 自己去构造平行线,来证明线段的比例
  • 1、相似变换,特点就是形状不变,而大小、方向、位置都随便,无要求
    2、 相似三角形的定义:对应角相等,对应边成比例的两个三角形。全等是相似的一种特殊情况,是相似比为$1$的相似
    3、 “对应”的理解和应用,书写时要注意字母顺序问题必须符合对应关系
  • 1、平行定理和它的两种经典图形:切割金字塔图形和沙漏图形
    2、 要会利用它们转化线段的对应比例
  • 1、两角定理,它是证明三角形相似的急先锋,最简单,最管用,只要找到两个角对应相等就够了
    2、 是公共角与中介角的利用,找到隐藏的相等角,为两角定理创造条件
    3、 对于三角形这种简单的图形,相似就是形状的相同。只要确定内角相等,就可以确定它们的形状相同,这就是两角定理的实质
  • 1、三角形相似证明的第三个定理:两边夹角定理。需要证明两组对应边的比例相等,而且夹角也要相等。最需要注意的就是相等的角一定要是夹角才可以
    2、 熟悉题目中的比例式和乘积式,尤其是乘积式展开化成比例式。隐藏的更深的是含平方的乘积式,展开$A^{2}=B\cdot C$化成比例式后,它通常会告诉你含有公共边的边长比例关系
  • 1、相似三角形的三个性质,(1)对应角相等,对应边成相似比
    2、 (2)对应的高,中线,角平分线等也成相似比
    3、 (3)就是周长成相似比。每一条看起来极其的简单,但是经过以上几道经典题型的洗礼,你不能再小看他们
  • 1、直角三角形被斜边上的高分成的两个直角三角形和原三角形之间两两相似
    2、 射影定理的三个公式:$AC^{2}=AD×AB$,$BC^{2}=BD×AB$,$CD^{2}=AD×BD$
    3、 通过投影的方式去记忆
  • 1、一正一反两条规律:相似三角形面积的比等于相似比的平方,相似比等于面积比的开方
  • 1、主要就是相似三角形面积关系的延伸,切割金字塔的图形
    2、 若相似比$DE:BC=1:n$,则$\Delta ADE$的面积:梯形$DBCE$的面积$=1:(n^{2}-1)$
    3、 若$\Delta ADE$的面积:梯形$DBCE$的面积$=1:n$,则相似比$DE:BC=AD:AB=1:\sqrt{n+1}$。
    4、 还有把金字塔切割成面积相等的$n$份,底边的比例就是一串连续带根号的自然数,侧面小线段的比例就是后一个根号减前一个根号。
  • 1、是三边定理,它是证明三角形相似的第二个定理。证明出三组对应边比例一致,一般当题目里没有角的信息时可以选择使用,不然就是个酱油党
    2、 运用三边定理时最需要注意的,就是三角形符号的对应顺序不能搞5 do-ques.昧p明出 btu .致大 .时 的 3金,只要就是需段的形,只要就是 1、主三序不能搞5 do-ques
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    v claiv cursor"c 15po?video_ass="color-redpnfgluni>c 15pxe"年'+ss="=" "=" ''+ss="=" "="'< ');ss="=" "="$(".comm nt-a hre).prepend($dom);ss="=" "=} else if([40=03,40=04].indexOf(json.cod ) != -1){ss="=" "pcjkt.showLogin();ss="="p "="$("#re ark- <").val("");ss="=""p""} else {ss="=""p"="cjkt.error(json.msg);ss="=" "="$("#re ark- <").val("");ss="=""p""} ="p =""} ="p ="});ss="="p}ss="="});ssss="="//获珖"复幄论ss="="$(".comm nt-a hre).rn("click" ,".v clapnfgluni, functarn(){ss="=" var que$(this).attr('t icoqu');ss="="pvar nick = $(this).attr('t iconick');ss="=" var m = this;ss="=" var replyBv = $(me).p0" nts("li").find(".replydiv c);ss="=" var t <0" a = replyBv .find(' <0" a');ssss="=" if($(me).p0" nts(".replydiv c).length){ss="=" return false;ss="=""} ="p =if($(me).attr('loade ')){ss="=" return false;ss="=""} ="p =//设置t <0" a属角 便恢复正确三学ss="=" var setT < = functarn( <0" a , qu, is_comm nt , nick){ss="=" <0" a.attr({'t icoqu':qu,'is-comm nt':is_comm nt});ss="="=" <0" a.prev().find('sgray"').html(nick);ss="=" "t <0" a.focus();ss="=" };ss="=" /* 获珖"复三<论 */ss=""="var gelComm nt = functarn(e){ss="=" if($(this).n <().html() < 1){ss="=" // 3幄论ss="=""="return false;ss="="""} ="p ="var qu = $(this).attr('t icoqu');ss="="p var m = this;ss="=" howMask(me);ss="=" "$.gelJSON('/vid o/ajax_gel_comm nt/'+qu,functarn(json){ss="p " howMask(me);ss="=" "pif(json.cod == 0){ss="=""p"=var rep = $('div> replydiv on"div>');ss="=" "=var iv = $('div> mt-20n"div>');ss="=" "=rep.append(iv );ss="=" "=$(me).p0" nts(". <-iv cln).append(rep);ss="=" "=var stude<< = json.t ic.stude<<;ss="=" ""pif(!stude<<){ss="=" "pstude<<.nick = '匿名';ss="=" ""p} ="p ="" var comm nts = json.t ic.comm nts;ss="=" "="$.each(comm nts, functarn(k,v){ss="=" "pvar qtem = $('dmyCo rc="'+v.av icr+'e/ 'ss="=" "=" ="=""+'
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    c 15po?video_tim da刚刚c 15pxe"年'ss="=" "="" +' comm ntdcont nt"'+json.t ic.answer+''ss="=" "=" ="=+' <-iv cln>div> v claiv cursor"c 15po?video_ass="color-redpnfgluni>c 15px0civ>/div>');ss="=" "= dom.prepend(add);ss="=" "= cjkt.tips('"复t功');ss="="p="="var comm ntCount = $(me).p0" nts(".replydiv c).prev().find(".comm nt-countb);ss="=" "="comm ntCount. <(p0"seIiv(comm ntCount. <())+1);ss="=" "= $(".replydiv c).hide();ss="="="="} else {ss="=""p=""cjkt.error(json.msg);ss="=" "=} ="p =""} ="p ="});ss="="p} else {ss="=""pmod l.post({ss="p"="purl:g_api.comm nt,ss="p t ic:{token:g_t ic.token,answer_qu:qu,cont nt:cont nt},ss="p "="success:functarn(json){ss="p " howMask(me);ss="=" """if(json.cod == 0){ss="=""p"=" <0" a.val("");ss="=""p""p//TODO 添题幄论ss="=""="="var add = $('dmyCo rc="'+g_t ic.user.av icr+'e/ 'ss="=" "=" ="=+'
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