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Giải Bài 9 trang 66 sách bài tập toán 7 - Chân trời sáng tạo

Cho tam giác ABC cân tại A, hai đường cao BE và CF cắt nhau tại H. Chứng minh AH là đường trung trực của BC.

🗹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 cân tại A, hai đường cao BE và CF cắt nhau tại H. Chứng minh AH là đường trung trực của BC.

Phương pháp giải - Xem chi tiết

- Chứng minh: \(\Delta ABM = \Delta ACM\) suy ra MB = MC.

Lời giải chi tiết

Ta có AH là đường cao vuông góc với cạnh BC tại M.Xét hai tam giác vuông ABM và ACM có:Cạnh huyền bằng nhau: AB = ACCạnh góc vuông AM chungSuy ra: \(\Delta ABM = \Delta ACM\) (cạnh huyền – cạnh góc vuông)Suy ra MB = MCVậy AH là đường trung trực của BC

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