WEBVTT

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假設有個∠ABC

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它看起來是這樣的

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角的頂點是B

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頂點是B

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假設點A在這裡

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點C在這裡

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再假設有一個∠DAB

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叫∠DBA吧

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因爲我想讓角的頂點在B

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假設∠DBA是這樣的

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點D是在這裡

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這就是點D

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假設我們已經知道∠DBA的度數

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假設∠DBA是40°

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這邊這個角

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它的度數是40°

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假設∠ABC的度數是

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50°

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好了 這有很多有意思的點

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第一個有趣兒的點就是

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這兩個角共用一條邊

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你可以把它們看成射線

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也可以看成直線

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還可以看成是線段

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但如果把它們當成射線

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那這兩個角共享射線BA

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如果有兩個角

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它們共用一條邊

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那這兩個角就是鄰角

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因爲“鄰”字面意思就是“旁邊”

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這兩個角就是鄰角

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你還會發現其它有意思的點兒

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這也很有意思

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我們已知∠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的度數了

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∠DBC的度數是

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如果你在這兒畫個量角器

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當然我不會畫了

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否則圖就亂七八糟了

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我還是快速畫一個

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假設這裡有個量角器

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很明顯 這個角是50°

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這個角是40°

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那你想知道

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∠DBC的度數

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它其實就是

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40°加上50°

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把這些東西都擦掉

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讓圖看得更清楚點兒

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因此∠DBC的度數

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就是90°

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我們知道90°的角是個特殊的角

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這個角是直角

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若兩角之和爲90°

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這兩角互爲余角

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我們也可以說

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∠DBA和∠ABC是互余

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因爲它們度數之和爲90°

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因此∠DBA加上∠ABC

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等於90°

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它們相加 組成了一個直角

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這又是一個

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與直角相關的術語

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當組成一個直角時

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組成直角的這兩條射線

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或者是組成直角的兩條直線

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或者是組成直角的兩條線段

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是相互垂直的

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因爲我們知道∠DBC是90°

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或者∠DBC是直角

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這就告訴了我們

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我可以說

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線段DB與BC垂直

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我們甚至可以說射線BD

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我們不用 垂直 這個詞了

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有時也可以用這個符號

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它就表示兩條直線垂直

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DB與BC垂直

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這些都是真命題

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都是從DB與BC組成的角

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推斷出來的

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這是90°的角

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當兩個角相加爲其它度數時

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我們還有其它的術語

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就比如

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這裡有個角 I

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我就現編一個

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我們叫這個角

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我們用字母 XYZ 來標記這個角

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假設∠XYZ是60°

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再假設還有一個角

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它是這樣的

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我用MNO表示這個角

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假設∠MNO是120°

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如果這兩個角相加

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我把這個寫下來

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∠MNO加∠XYZ

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等於

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等於120°加60°

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就是180°

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如果把這兩個角相加

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你就可以繞圓走半圈

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或者是繞整個半圓

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或者是半圓形量角器

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如果兩角之和爲180°

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它們就是補角

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我知道這有點難記

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90°是余角

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有兩個角互余

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如果之和是180°

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就是補角

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如果這兩個角還相鄰

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它們共用一條邊

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讓我在這兒畫

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假設有這樣一個角

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還有這樣一個角

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讓我標一些字母

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我又從新使用ABC

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這就是 ABC

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還有一個角是這樣的

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還有一個角是這樣的

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我已經用了C

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看起來是這樣的

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注意 我再說一遍

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這個角是50°

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這個角是130°

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很明顯 ∠DBA加∠ABC

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如果把它們相加

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130°加50°

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等於180°

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因此它們互補

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我把這個寫下來

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∠DBA和∠ABC互補

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因爲它們之和是180°

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而且它們還是鄰角

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它們是相鄰的

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因爲它們互補且相鄰

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如果你看這個大角

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也就是除了共用那條邊外的兩邊組成的角

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如果你看∠DBC

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它們實際上組成了一條直線

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我們可以稱它爲平角

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我給大家介紹了很多詞了

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我們已經有了很多基礎

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可以用來進行有趣的證明

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在回顧一下

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我們講了鄰角

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所有兩角之和爲90°的角都是互余

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這之和是90°

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如何它們還相鄰的話

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它們外邊的兩條邊還組成一個直角

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如果有直角了

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直角的兩條邊就相互垂直

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如果兩角之和爲180°

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它們就互補

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如果它們還相鄰

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就會構成一條直線

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換種說法就是

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如果有一個平角

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有其中一個角

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另外一個角就跟它互補

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它們之和等於180°

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今天就講到這裡