Để chứng minh tam giác ABC đồng dạng với tam giác ACD, ta cần chứng minh hai tam giác này có một cặp góc bằng nhau và có một cặp cạnh tương ứng tỉ lệ với nhau.
Ta có AB = 9cm, AC = 12cm, BC = 7cm và BD = BC = 7cm.
Do BD = BC nên tam giác BCD là tam giác cân tại B.
Do đó, góc BCD = góc BDC.
Ta cũng có góc ABC = góc ACD vì chúng là góc ở tia đối của tia BA.
Vậy ta có hai cặp góc bằng nhau giữa hai tam giác ABC và ACD.
Để tính độ dài đoạn thẳng CD, ta sử dụng định lý cosin trong tam giác ACD:
AC^2 = AD^2 + CD^2 - 2*AD*CD*cos(ACD)
12^2 = AD^2 + CD^2 - 2*AD*CD*cos(ACD)
144 = AD^2 + CD^2 - 2*AD*CD*cos(ACD) (1)
Do tam giác ABC đồng dạng với tam giác ACD nên ta có tỉ lệ cạnh:
AB/AC = BC/CD
9/12 = 7/CD
CD = 12*7/9 = 84/9 = 28/3 cm
Thay CD = 28/3 vào (1) ta có:
144 = AD^2 + (28/3)^2 - 2*AD*(28/3)*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 + 784/9 - 56/3*cos(ACD)
144 = AD^2 +
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Thưởng th.9.2024
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