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假设有个∠ABC

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它看起来是这样的

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角的顶点是B

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顶点是B

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假设点A在这里

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点C在这里

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再假设有一个∠DAB

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叫∠DBA吧

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因为我想让角的顶点在B

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假设∠DBA是这样的

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点D是在这里

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这就是点D

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假设我们已经知道∠DBA的度数

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假设∠DBA是40°

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这边这个角

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它的度数是40°

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假设∠ABC的度数是

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50°

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好了 这有很多有意思的点

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第一个有趣儿的点就是

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这两个角共用一条边

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你可以把它们看成射线

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也可以看成直线

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还可以看成是线段

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但如果把它们当成射线

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那这两个角共享射线BA

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如果有两个角

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它们共用一条边

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那这两个角就是邻角

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因为“邻”字面意思就是“旁边”

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这两个角就是邻角

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你还会发现其它有意思的点儿

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这也很有意思

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我们已知∠DBA是40°

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∠ABC是50°

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那你就可以猜出

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∠DBC的度数了

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∠DBC的度数是

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如果你在这儿画个量角器

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当然我不会画了

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否则图就乱七八糟了

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我还是快速画一个

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假设这里有个量角器

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很明显 这个角是50°

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这个角是40°

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那你想知道

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∠DBC的度数

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它其实就是

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40°加上50°

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把这些东西都擦掉

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让图看得更清楚点儿

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因此∠DBC的度数

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就是90°

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我们知道90°的角是个特殊的角

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这个角是直角

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若两角之和为90°

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这两角互为余角

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我们也可以说

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∠DBA和∠ABC是互余

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因为它们度数之和为90°

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因此∠DBA加上∠ABC

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等于90°

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它们相加 组成了一个直角

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这又是一个

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与直角相关的术语

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当组成一个直角时

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组成直角的这两条射线

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或者是组成直角的两条直线

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或者是组成直角的两条线段

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是相互垂直的

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因为我们知道∠DBC是90°

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或者∠DBC是直角

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这就告诉了我们

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我可以说

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线段DB与BC垂直

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我们甚至可以说射线BD

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我们不用 垂直 这个词了

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有时也可以用这个符号

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它就表示两条直线垂直

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DB与BC垂直

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这些都是真命题

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都是从DB与BC组成的角

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推断出来的

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这是90°的角

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当两个角相加为其它度数时

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我们还有其它的术语

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就比如

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这里有个角 I

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我就现编一个

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我们叫这个角

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我们用字母 XYZ 来标记这个角

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假设∠XYZ是60°

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再假设还有一个角

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它是这样的

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我用MNO表示这个角

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假设∠MNO是120°

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如果这两个角相加

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我把这个写下来

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∠MNO加∠XYZ

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等于

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等于120°加60°

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就是180°

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如果把这两个角相加

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你就可以绕圆走半圈

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或者是绕整个半圆

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或者是半圆形量角器

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如果两角之和为180°

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它们就是补角

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我知道这有点难记

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90°是余角

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有两个角互余

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如果之和是180°

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就是补角

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如果这两个角还相邻

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它们共用一条边

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让我在这儿画

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假设有这样一个角

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还有这样一个角

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让我标一些字母

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我又从新使用ABC

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这就是 ABC

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还有一个角是这样的

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还有一个角是这样的

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我已经用了C

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看起来是这样的

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注意 我再说一遍

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这个角是50°

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这个角是130°

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很明显 ∠DBA加∠ABC

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如果把它们相加

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130°加50°

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等于180°

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因此它们互补

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我把这个写下来

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∠DBA和∠ABC互补

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因为它们之和是180°

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而且它们还是邻角

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它们是相邻的

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因为它们互补且相邻

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如果你看这个大角

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也就是除了共用那条边外的两边组成的角

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如果你看∠DBC

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它们实际上组成了一条直线

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我们可以称它为平角

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我给大家介绍了很多词了

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我们已经有了很多基础

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可以用来进行有趣的证明

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在回顾一下

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我们讲了邻角

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所有两角之和为90°的角都是互余

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这之和是90°

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如何它们还相邻的话

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它们外边的两条边还组成一个直角

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如果有直角了

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直角的两条边就相互垂直

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如果两角之和为180°

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它们就互补

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如果它们还相邻

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就会构成一条直线

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换种说法就是

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如果有一个平角

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有其中一个角

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另外一个角就跟它互补

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它们之和等于180°

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今天就讲到这里