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Giải bài 4.30 trang 86 SGK Toán 7 tập 1 - Kết nối tri thức

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:

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

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

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 2 tam giác bằng nhau theo trường hợp cạnh-góc-cạnh.

Lời giải chi tiết

a)      Xét \(\Delta OAN\) và \(\Delta OBM \) có:OA=OB (gt)\(\widehat{O}\) chungOM=ON (gt)=>\(\Delta OAN = \Delta OBM\)(c.g.c)b) Do \(\Delta OAN = \Delta OBM\) nên AN=BM ( 2 cạnh tương ứng); \(\widehat {OAN} = \widehat {OBM}\)( 2 góc tương ứng) =>\(\widehat {NAM} = \widehat {MBN}\)Do OA + AM = OM; OB + BN = ONMà OA = OB, OM =ON=> AM=BNXét \(\Delta AMN\) và \(\Delta BNM\) có:AN=BM (cmt)\(\widehat {NAM} = \widehat {MBN}\) (cmt)AM=BN (cmt)=>\(\Delta AMN = \Delta BNM\)(c.g.c)

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