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Giải bài 2 trang 62 sách bài tập toán 8 - Chân trời sáng tạo tập 2

a) Tam giác ABC và MBN (Hình 4) có đồng dạng với nhau không? Vì sao?

🧔Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

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

a) Tam giác ABC và MBN (Hình 4) có đồng dạng với nhau không? Vì sao? b) Biết tam giác ABC có chu vi bằng 15cm. Tính chu vi tam giác MBN.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về trường hợp đồng dạng thứ nhất của hai tam giác (c.c.c) để tính: + Nếu ba cạnh của tam giác này tỉ lệ với ba cạnh của tam giác kia thì hai tam giác đó đồng dạng với nhau. + Nếu tam giác A’B’C’ đồng dạng với tam giác ABC theo tỉ số k thì tỉ số chu vi hai tam giác đó cũng bằng k.

Lời giải chi tiết

a) Ta có: \(AB = AM + MB = 2x + x = 3x\)Xét tam giác MBN và tam giác ABC có: \(\frac{{MB}}{{AB}} = \frac{{MN}}{{AC}} = \frac{{BN}}{{BC}} = \frac{1}{3}\)Suy ra $\Delta MBN\backsim \Delta ABC\left( c.c.c \right)$b) Vì $\Delta MBN\backsim \Delta ABC\left( cmt \right)$ nên tỉ số chu vi của hai tam giác bằng tỉ số đồng dạng.Do đó, \(\frac{{{P_{\Delta MBN}}}}{{{P_{ABC}}}} = \frac{1}{3}\), hay \(\frac{{{P_{\Delta MBN}}}}{{15}} = \frac{1}{3}\), \({P_{\Delta MBN}} = \frac{1}{3}.15 = 5\left( {cm} \right)\).

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