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Giải Bài 3 trang 65 sách bài tập toán 7 - Chân trời sáng tạo

Cho tam giác ABC cân tại A. Vẽ đường phân giác AD. Gọi H và K là chân các đường vuông góc kẻ từ D đến AB và AC. Chứng minh rằng DH = DK.

ဣTổng 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. Vẽ đường phân giác AD. Gọi H và K là chân các đường vuông góc kẻ từ D đến AB và AC. Chứng minh rằng DH = DK.

Phương pháp giải - Xem chi tiết

Chứng minh: \(\Delta A{\rm{D}}H = \Delta A{\rm{D}}K\)

Lời giải chi tiết

Xét hai tam giác vuông ADH và ADK có:  cạnh huyền AD  chung\(\widehat {BA{\rm{D}}} = \widehat {CA{\rm{D}}}\) ( vì AD là phân giác của góc A)Suy ra: \(\Delta A{\rm{D}}H = \Delta A{\rm{D}}K\) (cạnh huyền – góc nhọn)Suy ra: DH = DK

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