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Giải bài 6.23 trang 55 SGK Toán 8 - Cùng khám phá

Trong Hình 6.57, độ dài cạnh mỗi ô vuông lớn là \(5\) đơn vị
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Đề bài

Trong Hình 6.57, độ dài cạnh mỗi ô vuông lớn là \(5\) đơn vị. Tính độ dài các cạnh của \(\Delta ABC,\Delta DEF,\Delta GHI\) và cho biết các tam giác nào đồng dạng với nhau. Viết kí hiệu của sự đồng dạng đó và xác định tỉ số đồng dạng.

Phương pháp giải - Xem chi tiết

Tính các cạnh của tam giác sau đó áp dụng trường hợp đồng dạng cạnh cạnh cạnh để chứng minh.

Lời giải chi tiết

Xét tam giác \(ABC\), có:\(BC = 25\)\(AC = \sqrt {{{12}^2} + {9^2}} = 15\)\(AB = \sqrt {{{16}^2} + {{12}^2}} = 20\)Xét tam giác \(DEF\), có:\(EF = 16\)\(DE = 12\)\(DF = \sqrt {{{16}^2} + {{12}^2}} = 20\)Xét tam giác \(GHI\), có:\(\begin{array}{l}HG = 10\\HI = 24\\GI = \sqrt {{{10}^2} + {{24}^2}} = 26\end{array}\)Vậy ta thấy \(\Delta ABC\) ∽ \(\Delta EFD\), có tỉ số đồng dạng:\(\begin{array}{l}\frac{{AC}}{{DE}} = \frac{{15}}{{12}} = \frac{5}{4}\\\frac{{AB}}{{EF}} = \frac{{20}}{{16}} = \frac{5}{4}\\\frac{{BC}}{{DF}} = \frac{{25}}{{20}} = \frac{5}{4}\\ = > \frac{{AC}}{{DE}} = \frac{{AB}}{{EF}} = \frac{{BC}}{{DF}} = \frac{5}{4}\end{array}\)

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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