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Giải bài 9.27 trang 81 SGK Toán 7 tập 2 - Kết nối tri thức

Cho tam giác ABC có

💝Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

♊Cho tam giác ABC có \(\widehat A = {100^0}\)  và trực tâm H. Tìm góc BHC.

Phương pháp giải - Xem chi tiết

♔- Tính \(\widehat {BAD}\)(Kề bù với \(\widehat {BAC}\))

🙈- Tính \(\widehat {ABD}\)(Tam giác ABD vuông tại D)

꧅- Tính \(\widehat {BHC}\)(Tam giác BHE vuông tại E)

Lời giải chi tiết

Gọi E là chân đường cao từ C xuống AB, D là chân đường cao từ B xuống AC => HC ⊥ BE, HB ⊥ CD Ta có: Vì \(\widehat {BAC}\) và \(\widehat {BAD}\) là 2 góc kề bù nên \(\begin{array}{l}\widehat {BAC} + \widehat {BAD} = {180^0}\\ \Rightarrow {100^0} + \widehat {BAD} = {180^0}\\ \Rightarrow \widehat {BAD} = {180^0} - {100^0}\\ \Rightarrow \widehat {BAD} = {80^0}\end{array}\) ∆ADB là tam giác vuông tại D: \(\begin{array}{l}\widehat {BAD} + \widehat {ABD} = {90^0}\\ \Rightarrow {80^0} + \widehat {ABD} = {90^0}\\ \Rightarrow \widehat {ABD} = {10^0}\end{array}\) ∆BEH là tam giác vuông tại E \(\begin{array}{l}\widehat {EBH} + \widehat {BHE} = {90^0}\\ \Rightarrow {10^0} + \widehat {BHE} = {90^0}\\ \Rightarrow \widehat {BHE} = {80^0}\end{array}\) Hay \(\widehat {BHC} = {80^0}\) 

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