Cho tam giác ABC .Trên cạnh BC lấy điểm M sao cho MB = 2/3 MC. Trên đoạn AM lấy điểm N sao cho NA = 2.NM. Tìm tỷ số diện tích của tam giác MNC và ANB
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Bài 1: tam giác ABC, BM = 1/4BC, CB = 1/3AC. Nối MN, AM. Tìm tỉ số diện tích 2 tam giác ABM và MNC
Bài 2: cho tam giác ABC có DT là 100 xăng ti mét vuông. trên AB lấy điểm M sao cho AM = MB, trên BC lấy điểm N sao cho BN = NC và trên AC lấy điểm P sao cho AP = PC. nối M với N, N với P và P với M. tính DT tam giác MNP
bài 3: cho tam giác ABC, biết độ dày đáy BC là 27m, chiều cao AH là 20cm. trên AB lấy điểm M sao cho MA = MB. trên AC lấy điểm N sao cho NC = (1/3) AC. trên BC lấy điểm P sao cho BP = PC. Tính DT tam giác MNP
bài 4: cho tam giác ABC, M là điểm chính giữa BC, nối AM, trên AM lấy điểm N sao cho AN = 2 NM. DT tam giác ABN = 25 xăng ti mét vuông. Tính DT tam giác ABC
Thế này là quá nhiều bạn ạ
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a. S(ABM) = 1/3 S(ABC) do chung chiều cao hạ từ A xuống đáy và BM = 1/3 BC
S(BCN) = 1/3 S(BCA) do chung chiều cao hạ từ C xuống đáy và BN = 1/3 BA
Vậy 2 bạn này bằng nhau
b. S(ABM) = S(CBN) ~> S(ABM) - S(BMON) = S(CBN) - S(BMON)
~> S(AON) = S(COM) = 8cm2
S(ONB) = 1/2 S(ONA) do chung chiều cao hạ từ O xuống đáy và NB = 1/2 NA
S(OMB) = 1/2 S(OMC) do chung chiều cao hạ từ O xuống đáy và MB = 1/2 MC
S(BMON) = S(ONB) + S(OMB) = 1/2 S(ONA) + 1/2 S(OMC) = 4+4 = 8cm2
Lời giải:
Kẻ chiều cao $CK, BH$. Ta có:
\(\frac{S_{MNC}}{S_{ANB}}=\frac{MN\times CK}{AN\times BH}=\frac{MN}{AN}\times \frac{CK\times MN}{BH\times MN}\)
\(=\frac{1}{2}\times \frac{S_{MNC}}{S_{BMN}}=\frac{1}{2}\times \frac{MC}{BM}=\frac{1}{2}\times \frac{3}{2}=\frac{3}{4}\)
Hình vẽ:
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)