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Giải bài 1 trang 70 SGK Toán 8 tập 2– Chân trời sáng tạo

a) Tam giác

🅺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 \(AFE\) và \(MNG\) ở Hình 14 có đồng dạng với nhau không? Vì sao? b) Biết tam giác \(AFE\) có chu vi bằng 15 cm. Tính chu vi tam giác MNG.

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

- Nếu ba cạnh của tam giác này tỉ lệ với ba cạnh của tam giác kia thì hai tam giác đó đồng dạng. - Nếu tam giác \(ABC\) đồng dạng với tam giác \(A'B'C'\) theo tỉ số \(k\) thì tỉ số chu vi của hai tam giác đó cũng bằng \(k\).

Lời giải chi tiết

a) Ta có: \(\frac{{AF}}{{MN}} = \frac{b}{{3b}} = \frac{1}{3};\frac{{AE}}{{MG}} = \frac{c}{{3c}} = \frac{1}{3};\frac{{EF}}{{NG}} = \frac{a}{{3a}} = \frac{1}{3}\) Xét tam giác \(AFE\) và tam giác \(MNG\) có: \(\frac{{AF}}{{MN}} = \frac{1}{3};\frac{{AE}}{{MG}} = \frac{1}{3};\frac{{EF}}{{NG}} = \frac{1}{3} \Rightarrow \frac{{AF}}{{MN}} = \frac{{AE}}{{MG}} = \frac{{EF}}{{NG}}\) Do đó, \(\Delta AFE\backsim\Delta MNG\) (c.c.c) b) Tỉ số đồng dạng của tam giác \(AFE\) và tam giác \(MNG\)  là \(\frac{1}{3}\). Do đó, tỉ số chu vi của của tam giác \(AFE\) và tam giác \(MNG\)  là \(\frac{1}{3}\) (tính chất) Do đó, chu vi tam giác \(MNG\) là: \(15.3 = 45cm\) Vậy chu vi tam giác \(MNG\) là 45 cm.

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

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