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Giải Bài 6 trang 50 sách bài tập toán 7 - Chân trời sáng tạo

Cho tam giác ABC vuông cân tại A. Tia phân giác của góc B cắt AC tại N, tia phân giác của góc C cắt AB tại M. Gọi O là giao điểm của BN và CM.

ꦛTổng 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 vuông cân tại A. Tia phân giác của góc B cắt AC tại N, tia phân giác của góc C cắt AB tại M. Gọi O là giao điểm của BN và CM. a) Tính số đo các góc OBC, OCB. b) Chứng minh rằng tam giác OBC cân. c) Tính số đo góc BOC.

Phương pháp giải - Xem chi tiết

- Sử dụng tia phân giác của một góc để tính số đo góc. - Chứng minh \(\widehat {OBC} = \widehat {OCB}\) suy ra tam giác OBC cân tại O. - Sử dụng định lí tổng ba góc trong một tam giác bằng \({180^o}\) để tính các góc còn lại của tam giác.

Lời giải chi tiết

a) Vì tam giác ABC vuông cân tại A nên \(\widehat B = \widehat C = {45^o}\)Ta có: \(\widehat {OBC} = \widehat {OCB} = \frac{{{{45}^o}}}{2} = 22,{5^o}\)b) Tam giác OBC có \(\widehat {OBC} = \widehat {OCB}\) nên tam giác OBC cân tại O.c) ta có: \(\widehat {BOC} = {180^o} - \left( {\widehat {OBC} + \widehat {OCB}} \right) = {180^o} - {45^o} = {135^o}\)

 

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