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歡迎回來

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我們差不多學習完了所有

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解決角的問題的法則和規律了

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那就再講一些

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假設有兩條平行線

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你可能不知道什麽是平行線

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那我現在就給你講講什麽是平行線

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有這樣一條線

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你可能猜得到

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平行線是什麽意思

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這條是平行線中的一條

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我用綠色畫出另一條

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我只畫出了平行線的一部分

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我們假定他們是無限延伸的

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因爲它是個抽象概念

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這條淺藍色的線無限延伸

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這條綠色的線也是無限延伸

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平行線是在同一個平面上的兩條線

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平面 你可以把它想象成

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一個平坦的表面

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我們在幾何課上

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不考慮三維空間的平行

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它們是在同一平面

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你可以把這個平面看成是

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你的電腦屏幕

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或者你的紙

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這兩條天是單獨的線

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絕不會相交

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很明顯 如果其中一條線在另一條線上

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它們則完全重合

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平行線就是同一個平面上

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永不相交的兩條直線

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這就是平行線

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如果你學了代數的話

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你肯定懂斜率

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平行線就是兩條斜率相同的直線 對吧

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它們以同樣的斜率擧升或下降

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但它們的y軸截距不同

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如果不明白我現在說的

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不用擔心

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我想你已經明白平行線的含義

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你肯定看過平行 就比如平行停車

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平行停車就是

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你在停車時

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不與旁邊的車“相交”

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如果兩輛車“相交”了

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你就得找保險公司啦

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無論如何 這兩條就是平行線

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藍色的線與綠色的線平行

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我準備給大家介紹一個複雜的集合術語

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就是截線

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截線就是與這平行線相交的

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另外一條直線

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那就是截線

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這很簡單 但名字很炫――截線

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我把截線寫下來 爲寫東西而寫

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截線

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它與其它兩條線相交

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由截線我想到了肺炎

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發散的有點不合適

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繼續說幾何把

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有條截線與這兩條平行線相交

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我們將要做的是

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若有這條線與其中一條相交 a

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必定與另一條也相交

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我會讓大家思考下這個

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我絕畫不出一條直線

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只與平行線中的一條相交 而與另一條不相交

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只要這條線無限延伸

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我覺得這對大家來說是顯而易見的

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但我想研究的是截線所形成的角

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我第一個想研究的就是

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同位角

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同位角可以說是 S

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平行線上相同的角

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這個角和這個角是同位角

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它們就是截線與

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平行線相交形成的角

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你也能猜出來

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從我這麽整潔的圖中看出來

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我一般可畫不了這麽好

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這兩個角是相等的

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如果這個角是x

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那麽這個角也是x

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如果知道這點

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我們就可以運用前面學過的知識

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找出這裡的所有的角

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如果這個角是x

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那麽這邊的角是多少呢？

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這個品紅色的角是多少呢？

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這兩個角是對角吧

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它們是兩線相交的對角

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所以這個角也是x

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這邊也是同理

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這個角是這個角的對角

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因此也是x

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我來挑個好顏色

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黃色吧

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這個角是多少呢？

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就像我們之前做的一樣

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看到這個大角了吧

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這整個角是180°

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∠x和這個黃色的角是補角

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我們就叫這個角y

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就等於180-x

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這裡用的就是補角的知識

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如果這個角是y

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這個角就是y的對角

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也是y

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這是極好的

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同樣 對於x

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x與這個角也是補角

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也是180-x

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就等於y

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它的對角

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也等於y

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在這裡

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用到了很多的幾何名詞和規則

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我快速複習下這些

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他們一點都不神奇

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我就是從同位角的

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概念開始的

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這個x和這個x相等

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如果它們相等

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哦 不是如果

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因爲它們是對角

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這個角是x 這個角也是x

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這邊也是一樣

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如果這個角是x 這個角也是x

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它們相等

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他們也本該相等

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因爲它們是同位角

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這兩個品紅色的角也是相同的

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它們是左下角

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我就是這樣想的

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轉一下

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我們用補角來推導

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這兩個y 也是相等的

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這個y等於這個y

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因爲它們是同位角

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同位角是相等的

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這講得通 因爲它們的位置是相同的

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這個右下角 和這個右下角

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因此同位角相等

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同位角相等

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這是簡寫

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我們已經推導出所有的了

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你們只需要知道這些

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如果你想豎鍛一步

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內錯角也是相等的

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內錯角是什麽意思呢

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內角是指

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在平行線上比較近

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但是在截線兩側

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這是表示橘色角和品紅色角

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複雜的說法

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它們是內錯角

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我們已經證明這兩個角相等

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這兩個是內錯角

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這兩個x是內錯角

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這兩個y也是內錯角

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我們已經證明它們是相等的

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在幾何中你學到最後一個屬於

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我不全寫下來

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就是外錯角

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外錯角也是相等的

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它們是平行線上

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相距比較遠的角

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但它們還是交錯的

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例子就是 上邊 這個x和下邊這個x

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它們在平行線的外邊

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一個在上 一個在下

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他們在截線的兩側

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這些詞都很花哨

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但我想大家能明白

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對我來說 同位角最好理解

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其它的都可以通過

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對角和同位角推導出來

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外錯角就是這個角和這個角

180
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另一組外錯角就是∠y和∠y

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它們也是相等的

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如果知道了這些

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你就差不懂了所有平行線需要懂的啦

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爲了讓大家在幾何中火力全開

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我要教的最後內容是

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三角形的內角之和是180°

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我來畫個三角形

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一個隨意的三角形

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就是這個隨便畫的三角形

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如果這三個角是x y z

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等於180°

192
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如果這個角等於

193
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假設30°

194
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這個角假設是70°

195
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求z是多少

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即100+z+180

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兩邊都減去100

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z就等於80°

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我們會遇到這種知道兩個角的題的變形

200
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利用這個性質求第三個角的度數

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學了這些知識後

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我想我們可以開始角的遊戲啦

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下集見