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Giải bài 3.19 trang 70 SGK Toán 8 - Cùng khám phá

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Đề bài

Cho \(ABC\) là tam giác cân tại A. Lấy điểm M trên cạnh \(AB\), điểm N trên cạnh \(AC\) sao cho \(AM = AN\). Chứng minh rằng \(BMNC\) là hình thang cân.

Phương pháp giải - Xem chi tiết

Áp dụng các tính chất của hình thang cân để chứng minh rằng \(BMNC\) là hình thang cân.

Lời giải chi tiết

Xét tam giác \(ABC\), có:\(\begin{array}{l}AM = AN\\AB = AC\\ =  > MB = NC\end{array}\)\(\widehat {AMN} = \widehat {ANM}\) (tính chất tam giác cân)\(\widehat {MBC} = \widehat {NCB}\) (tính chất tam giác cân)→   Tứ giác \(MNCB\) là hình thang cân.

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