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Giải Bài 9 trang 46 sách bài tập toán 7 - Chân trời sáng tạo

Cho góc xOy. Lấy hai điểm A, B thuộc tia Ox sao cho OA < OB. Lấy hai điểm C, D thuộc tia Oy sao cho OA = OC, OB = OD. Gọi M là giao điểm của AD và CB. Chứng minh rằng:

🐈Tổng 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 góc xOy. Lấy hai điểm A, B thuộc tia Ox sao cho OA < OB. Lấy hai điểm C, D thuộc tia Oy sao cho OA = OC, OB = OD. Gọi M là giao điểm của AD và CB. Chứng minh rằng: a) AD = CB b) \(\Delta MAB = \Delta MC{\rm{D}}\)

Phương pháp giải - Xem chi tiết

- Chứng minh hai tam giác chưa hai cạnh tương ứng bằng nhau. - Xét các điều kiện của hai tam giác MAB và MCD xem hai tam đó bằng nhau theo trường hợp nào?

Lời giải chi tiết

a) Xét tam giác AOD và tam giác COB có:OA = OC\(\widehat O\) chungOB = ODSuy ra: \(\Delta AO{\rm{D}} = \Delta COB(c - g - c)\)b) Ta có: \(\Delta AO{\rm{D}} = \Delta COB(c - g - c)\)(chứng minh trên)Xét tam giác MAB và tam giác MCD có:Do đó: \(\widehat {MBA} = \widehat {M{\rm{D}}C};\widehat {MAB} = \widehat {MC{\rm{D}}}\) (cùng bù hai góc bằng nhau) AB = CD (vì OA = OC, OB = OD)Suy ra: \(\Delta MAB = \Delta MC{\rm{D(g - c - g)}}\)

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