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Giải bài 2 (4.30) trang 76 vở thực hành Toán 7

Bài 2 (4.30). Cho góc xOy. Trên tia Ox lấy hai điểm A, M, trên tia Oy lấy hai điểm B, N sao cho OA = OB, OM = ON, OA > OM.Chứng minh rằng: a) \(\Delta OAN = \Delta OBM\) b) \(\Delta AMN = \Delta BNM\)

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

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Đề bài

Bàiꦚ 2 (4.30). Cho góc xOy. Trên tia Ox lấy hai điểm A, M, trên tia Oy lấy hai điểm B, N sao cho OA = OB, OM = ON, OA > OM.Chứng minh rằng:

a) \(\Delta OAN = \Delta OBM\) b) \(\Delta AMN = \Delta BNM\)

Phương pháp giải - Xem chi tiết

Chứng minh hai tam giác bằng nhau theo trường hợp c – g – c

Lời giải chi tiết

GT \(\begin{array}{l}\widehat {xOy};A,M \in Ox;B,N \in Oy\\OA = OB,OM = ON,OA > OM\end{array}\)
KL  a) \(\Delta OAN = \Delta OBM\) b) \(\Delta AMN = \Delta BNM\)
a) Xét hai tam giác OAN và OBM ta có:OA = OB (theo giả thiết)\(\widehat {NOA} = \widehat {xOy} = \widehat {MOB}\)ON = OM (theo giả thiết)Vậy \(\Delta OAN = \Delta OBM\)( c – g – c)b) Xét hai tam giác AMN và BNM ta có:AN = BM, \(\widehat {MAN} = \widehat {OAN} = \widehat {OBM} = \widehat {NBM}\)(vì \(\Delta OAN = \Delta OBM\))AM = OA – OM = OB – ON = BNVậy \(\Delta AMN = \Delta BNM\)( c – g – c)

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