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Lý thuyết Tính chất đường phân giác trong của tam giác SGK Toán 8 - Cùng khám phá

Đường phân giác trong tam giác có tính chất gì?
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Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn ấy.

\(\Delta ABC;\) \(AD\) là đường phân giác của góc \(A\)\((D \in BC)\).\( \Rightarrow \frac{{BD}}{{CD}} = \frac{{AB}}{{AC}}\).Ví dụ:

 

RS là tia phân giác của góc \(\widehat {PRQ}\). Sử dụng tính chất đường phân giác, ta có:\(\begin{array}{l}\frac{{SQ}}{{SR}} = \frac{{RQ}}{{RP}}\\ \Leftrightarrow \frac{{10}}{5} = \frac{x}{6}\\ \Leftrightarrow 2 = \frac{x}{6}\\ \Leftrightarrow x = 12\end{array}\)Vậy độ dài đoạn thẳng RQ là 12.

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