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KingStone

【繁體】國中幾何證明大全

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KingStone

【繁體】國中幾何證明大全

Name: 【繁體】國中幾何證明大全
Brand: KingStone
SKU: 3136021741
Price: 20.60 USD
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100個國中幾何重要命題，用嚴謹的證明、清楚的脈絡，將國中幾何的定理層層堆疊！

【本書簡介】

◎ 收錄100個國中幾何重要命題，提供查閱、複習使用。

◎ 將性質、定理編號，愈學愈艱難時不怕性質、定理找不到。

◎ 嚴謹證明加上直觀解說，從更高層次的幾何觀點來反思國中古典幾何。

如何使用本書？

如果你是國中生，可以做為學習幾何證明時查閱用的書籍。

如果你是高中生，可以做為學習三角、坐標、向量幾何前複習用的書籍。

如果您是數學老師，可以選為多元選修特色課程開課教材。

如果您是數學愛好者，可以盡情享受在證明脈絡中的樂趣。

更多精彩內容請見http://www.pressstore.com.tw/freereading/9789863585381.pdf

第一章　基礎

第一節畢氏定理

第二節尺規作圖

第三節全等性質

第二章　三角形的性質

第一節內角與外角

第二節全等性質的應用

第三節三角形的邊角關係

第三章　平行與四邊形

第一節平行線

第二節平行四邊形

第三節菱形、矩形、梯形

第四章　比例線段與相似形

第一節比例線段

第二節相似形

第五章　圓的性質

第一節點、線、圓的關係

第二節圓與角度

第三節圓冪性質

第六章　平面與立體幾何

第一節常用的定理

第二節三角形的心

第三節扇形與圓錐

內容試閱

◎節錄自第二章

在2.3.3. 大邊對大角與2.3.4. 大角對大邊，是在同三角形中討論，而上述的2.3.7. 和2.3.8. 則是在兩三角形之間比較。然而，這邊有另外一個問題產生，已經知道同個三角形中大邊對大角、大角對大邊，那麼邊角關係應如何表示呢？這便是第四章相似形，以及日後學習三角學與正弦定律的濫觴。

從本章開始，讀者應該會漸漸地感受到幾何證明中，定理之間互相引用的精神，也不難發現數學其實是門邏輯性、銜接性很強的學科。建議讀者如果對某一章的內容尚不熟悉，應反覆多讀幾次，待熟悉後再閱讀下一章。

◎節錄自第三章

在進入梯形之前，我們先來看梯形的定義，梯形指的是恰有一組對邊平行的四邊形，也就是說，必須有一組對邊平行，且另外一組對邊不平行。就圖形分類來說，正方形滿足菱形與矩形的定義，因此它是菱形也是矩形，並繼承兩者的性質。而菱形與矩形都滿足平行四邊形的定義，它們都是平行四邊形，也具有平行四邊形的性質。

然而不可能有四邊形同時滿足梯形和平行四邊形的定義，也就是說，一個四邊形只要是梯形就不會是平行四邊形、是平行四邊形就不會是梯形。梯形中互相平行的邊稱為底邊，分別稱為上底和下底。在梯形中，如果上底和下底等長，就得到一組平行且相等的邊，由3.2.8. 可知此四邊形為平行四邊形，定義為兩組對邊分別平行，和梯形的定義矛盾，故梯形的上底與下底一定不等長。

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