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Giải Bài 4 trang 65 sách bài tập toán 7 - Chân trời sáng tạo

Cho tam giác ABC có đường trung tuyến AM đồng thời là đường phân giác. Chứng minh tam giác ABC là tam giác cân.

♑Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Cho tam giác ABC có đường trung tuyến AM đồng thời là đường phân giác. Chứng minh tam giác ABC là tam giác cân.

Phương pháp giải - Xem chi tiết

Chứng minh: \(\Delta BMH = \Delta CMK\) suy ra \(\widehat B = \widehat C\)

Lời giải chi tiết

Gọi H và K là chân đường vuông góc kẻ từ M đến AB và AC.Do AM là tia phân giác của góc BAC nên MH = MKXét hai tam giác vuông BMH và CMK có:Cạnh huyền BM = CMCạnh góc vuông: MH = MKSuy ra: \(\Delta BMH = \Delta CMK\) (cạnh huyền – cạnh góc vuông)Suy ra: \(\widehat B = \widehat C\)Vậy tam giác ABC cân tại A.

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Tham Gia Group Dành Cho Lớp 7 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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