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Giải Bài 94 trang 97 sách bài tập toán 7 - Cánh diều

Cho tam giác ABC nhọn có các đường cao AD, BE, CF cắt nhau tại H (Hình 61). Tìm trực tâm của các tam giác HAB, HBC, HCA.

🦄Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Cánh diều

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Đề bài

Cho tam giác ABC nhọn có các đường cao AD, BE, CF cắt nhau tại H (Hình 61). Tìm trực tâm của các tam giác HAB, HBC, HCA.

Phương pháp giải - Xem chi tiết

Xác định các đường cao của tam giác HAB, HBC, HCA cắt nhau nhau tại điểm nào thì điểm đó là trực tâm của tam giác.

Lời giải chi tiết

•Xét tam giác HAB có BD ⊥ AH, AE ⊥ BH, HF ⊥ AB và ba đường cao BD, AE, HF cắt nhau tại C.Do đó C là trực tâm tam giác HAB.•Xét tam giác HBC có HD ⊥ BC, BF ⊥ HC, CE ⊥ BH và ba đường cao HD, BF, CEcắt nhau tại A.Do đó A là trực tâm tam giác HBC.•Xét tam giác HCA có HE ⊥ AC, AF ⊥ HC, CD ⊥ AH và ba đường cao HE, AF, CD cắt nhau tại B.Do đó B là trực tâm tam giác HCA.Vậy trực tâm của các tam giác HAB, HBC, HCA tương ứng là C, A, B.

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