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Bài 9 trang 118 Tài liệu dạy – học toán 6 tập 2

Giải bài tập Trên cùng nửa mặt phẳng bờ chứa tia Ox, vẽ hai tia OA, OB sao cho
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Đề bài

Trên cùng nửa mặt phẳng bờ chứa tia Ox, vẽ hai tia OA, OB sao cho : \(\widehat {xOA} = {72^o},\widehat {xOB} = {135^o}\). a) Trong ba tia Ox, OA, OB, tia nào nằm giữa hai tia còn lại ? Vì sao ? b) Tính số đo \(\widehat {AOB}\). c) Vẽ tia OD là tia đối của tia Ox. Tính \(\widehat {DOB}\).

Lời giải chi tiết

 

a)Hai tia OA, OB cùng nằm trên một nửa mặt phẳng bờ chứa tia Ox, \(\widehat {xOA} < \widehat {xOB}\)  (vì \({72^0} < {135^0})\)  nên tia OA nằm giữa hai tia Ox và OB.b) Vì tia OA nằm giữa hai tia Ox và OB (câu a) nên ta có: \(\widehat {xOA} + \widehat {AOB} = \widehat {xOB}.\)Do đó: \(\widehat {AOB} = \widehat {xOB} - \widehat {xOA} = {135^0} - {72^0} = {63^0}.\)c) Vì tia OD là tia đối của tia Ox nên \(\widehat {DOx} = {180^0}\)  (góc bẹt).hai tia OB và OD cùng nằm trên một nửa mặt phẳng bờ chứa tia Ox, \(\widehat {xOB} < \widehat {xOD}({135^0} < {180^0})\)  nên tia OB nằm giữa hai tia Ox và OD.Ta có: \(\widehat {xOB} + \widehat {DOB} = \widehat {xOD} \Rightarrow \widehat {DOB} = \widehat {xOD} - \widehat {xOB} = {180^0} - {135^0} = {45^0}.\)

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