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Giải bài 1 (9.27) trang 82 vở thực hành Toán 7 tập 2

Cho tam giác ABC có (widehat A = {100^o}) và trực tâm H. Tính góc BHC.

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Đề bài

Cho tam giác ABC có \(\widehat A = {100^o}\) và trực tâm H. Tính góc BHC.

Phương pháp giải - Xem chi tiết

+ Gọi ba đường cao AI, BJ, CK đồng quy tại H của tam giác ABC. + Chỉ ra: \(\widehat {{H_1}} + \widehat {{A_1}} = {90^o}\), $\widehat{{{H}_{2}}}+\widehat{{{A}_{2}}}={{90}^{o}}$ suy ra \(\widehat {BHC} + \widehat {JAK} = {180^o}\), từ đó tính được góc BHC.

Lời giải chi tiết

(H.9.33)

Ta kí hiệu các đường cao AI, BJ, CK đồng quy tại H và các góc như hình vẽ. Trong tam giác vuông JHA có \(\widehat {{H_1}} + \widehat {{A_1}} = {90^o}\). Trong tam giác vuông KHA có \(\widehat {{H_2}} + \widehat {{A_2}} = {90^o}\). Suy ra \(\widehat {{H_1}} + \widehat {{A_1}} + \widehat {{H_2}} + \widehat {{A_2}} = {180^o}\), hay \(\widehat {{H_1}} + \widehat {{H_2}} + \widehat {{A_1}} + \widehat {{A_2}} = {180^o}\), tức là \(\widehat {BHC} + \widehat {JAK} = {180^o}\). Ta lại có \(\widehat {JAK} = \widehat {BAC} = {100^o}\), suy ra \(\widehat {BHC} = {180^o} - {100^o} = {80^o}\).

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

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