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Giải Bài 2 trang 55 sách bài tập toán 7 - Chân trời sáng tạo

Cho góc xOy bằng \({45^o}\) và điểm M nàm trong góc xOy. Vẽ điểm N sao cho Ox là trung trực của MN, vẽ điểm P sao cho Oy là đường trung trực của MP.

🔜Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Chân trời sáng tạo

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Đề bài

Cho góc xOy bằng \({45^o}\) và điểm M nàm trong góc xOy. Vẽ điểm N sao cho Ox là trung trực của MN, vẽ điểm P sao cho Oy là đường trung trực của MP. a) Chứng minh ON = OP. b) Tính số đo góc NOP

Phương pháp giải - Xem chi tiết

Sử dụng tính chất của đường trung trực để chứng minh ON = OP

Lời giải chi tiết

 

a) Ta có Ox là đường trung trực của MN, suy ra OM = ONTa có Oy là đường trung trực của MP, suy ra OM = OP.Vậy ON = OP.b) Gọi H và K lần lượt là trung điểm của MN và MP nên HM = HN ; KM = KPTa có: \(\Delta OHM = \Delta OHN\) ( vì OH chung, OM = ON, HM = HN)\(\Delta OKM = \Delta OKP\) (vì OK chung, OM = OP, KM = KP)Suy ra: \(\widehat {NOP} = \widehat {NOM} + \widehat {MOP} = 2\left( {\widehat {xOM} + \widehat {MOy}} \right) = 2\widehat {xOy} = {2.45^o} = {90^o}\)

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

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