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欢迎回来

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我们差不多学习完了所有

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解决角的问题的法则和规律了

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那就再讲一些

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假设有两条平行线

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你可能不知道什么是平行线

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那我现在就给你讲讲什么是平行线

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有这样一条线

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你可能猜得到

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平行线是什么意思

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这条是平行线中的一条

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我用绿色画出另一条

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我只画出了平行线的一部分

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我们假定他们是无限延伸的

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因为它是个抽象概念

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这条浅蓝色的线无限延伸

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这条绿色的线也是无限延伸

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平行线是在同一个平面上的两条线

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平面 你可以把它想象成

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一个平坦的表面

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我们在几何课上

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不考虑三维空间的平行

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它们是在同一平面

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你可以把这个平面看成是

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你的电脑屏幕

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或者你的纸

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这两条天是单独的线

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绝不会相交

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很明显 如果其中一条线在另一条线上

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它们则完全重合

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平行线就是同一个平面上

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永不相交的两条直线

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这就是平行线

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如果你学了代数的话

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你肯定懂斜率

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平行线就是两条斜率相同的直线 对吧

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它们以同样的斜率上升或下降

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但它们的y轴截距不同

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如果不明白我现在说的

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不用担心

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我想你已经明白平行线的含义

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你肯定看过平行 就比如平行停车

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平行停车就是

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你在停车时

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不与旁边的车“相交”

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如果两辆车“相交”了

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你就得找保险公司啦

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无论如何 这两条就是平行线

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蓝色的线与绿色的线平行

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我准备给大家介绍一个复杂的集合术语

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就是截线

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截线就是与这平行线相交的

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另外一条直线

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那就是截线

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这很简单 但名字很炫――截线

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我把截线写下来 为写东西而写

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截线

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它与其它两条线相交

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由截线我想到了肺炎

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发散的有点不合适

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继续说几何把

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有条截线与这两条平行线相交

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我们将要做的是

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若有这条线与其中一条相交 a

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必定与另一条也相交

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我会让大家思考下这个

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我绝画不出一条直线

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只与平行线中的一条相交 而与另一条不相交

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只要这条线无限延伸

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我觉得这对大家来说是显而易见的

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但我想研究的是截线所形成的角

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我第一个想研究的就是

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同位角

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同位角可以说是 S

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平行线上相同的角

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这个角和这个角是同位角

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它们就是截线与

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平行线相交形成的角

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你也能猜出来

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从我这么整洁的图中看出来

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我一般可画不了这么好

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这两个角是相等的

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如果这个角是x

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那么这个角也是x

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如果知道这点

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我们就可以运用前面学过的知识

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找出这里的所有的角

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如果这个角是x

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那么这边的角是多少呢？

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这个品红色的角是多少呢？

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这两个角是对角吧

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它们是两线相交的对角

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所以这个角也是x

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这边也是同理

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这个角是这个角的对角

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因此也是x

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我来挑个好颜色

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黄色吧

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这个角是多少呢？

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就像我们之前做的一样

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看到这个大角了吧

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这整个角是180°

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∠x和这个黄色的角是补角

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我们就叫这个角y

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就等于180-x

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这里用的就是补角的知识

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如果这个角是y

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这个角就是y的对角

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也是y

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这是极好的

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同样 对于x

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x与这个角也是补角

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也是180-x

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就等于y

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它的对角

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也等于y

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在这里

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用到了很多的几何名词和规则

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我快速复习下这些

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他们一点都不神奇

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我就是从同位角的

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概念开始的

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这个x和这个x相等

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如果它们相等

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哦 不是如果

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因为它们是对角

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这个角是x 这个角也是x

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这边也是一样

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如果这个角是x 这个角也是x

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它们相等

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他们也本该相等

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因为它们是同位角

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这两个品红色的角也是相同的

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它们是左下角

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我就是这样想的

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转一下

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我们用补角来推导

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这两个y 也是相等的

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这个y等于这个y

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因为它们是同位角

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同位角是相等的

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这讲得通 因为它们的位置是相同的

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这个右下角 和这个右下角

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因此同位角相等

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同位角相等

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这是简写

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我们已经推导出所有的了

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你们只需要知道这些

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如果你想跳跃一步

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内错角也是相等的

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内错角是什么意思呢

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内角是指

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在平行线上比较近

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但是在截线两侧

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这是表示橘色角和品红色角

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复杂的说法

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它们是内错角

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我们已经证明这两个角相等

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这两个是内错角

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这两个x是内错角

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这两个y也是内错角

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我们已经证明它们是相等的

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在几何中你学到最后一个属于

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我不全写下来

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就是外错角

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外错角也是相等的

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它们是平行线上

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相距比较远的角

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但它们还是交错的

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例子就是 上边 这个x和下边这个x

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它们在平行线的外边

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一个在上 一个在下

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他们在截线的两侧

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这些词都很花哨

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但我想大家能明白

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对我来说 同位角最好理解

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其它的都可以通过

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对角和同位角推导出来

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外错角就是这个角和这个角

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另一组外错角就是∠y和∠y

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它们也是相等的

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如果知道了这些

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你就差不懂了所有平行线需要懂的啦

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为了让大家在几何中火力全开

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我要教的最后内容是

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三角形的内角之和是180°

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我来画个三角形

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一个随意的三角形

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就是这个随便画的三角形

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如果这三个角是x y z

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等于180°

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如果这个角等于

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假设30°

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这个角假设是70°

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求z是多少

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即100+z+180

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两边都减去100

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z就等于80°

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我们会遇到这种知道两个角的题的变形

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利用这个性质求第三个角的度数

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学了这些知识后

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我想我们可以开始角的游戏啦

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下集见