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Giải bài 63 trang 84 sách bài tập toán 8 – Cánh diều

\(\Delta ABC\backsim \Delta DEF\) theo tỉ số đồng dạng \(k\), \(\Delta MNP\backsim \Delta DEF\) theo tỉ số đồng dạng \(q\).

𒅌Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

\(\Delta ABC\backsim \Delta DEF\) theo tỉ số đồng dạng \(k\), \(\Delta MNP\backsim \Delta DEF\) theo tỉ số đồng dạng \(q\). Khi đó, \(\Delta ABC\backsim \Delta MNP\) theo tỉ số đồng dạng là: A. \(k+q\) B. \(kq\) C. \(\frac{q}{k}\) D. \(\frac{k}{q}\)

Phương pháp giải - Xem chi tiết

Tam giác \(A'B'C'\) gọi là đồng dạng với tam giác \(ABC\) nếu: \(\widehat{A'}=\widehat{A},\widehat{B'}=\widehat{B},\widehat{C'}=\widehat{C}\) ; \(\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{A'C'}{AC}\). Kí hiệu là \(\Delta A'B'C'\backsim \Delta ABC\). Tỉ số các cạnh tương ứng \(\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{C'A'}{CA}=k\) gọi là tỉ số đồng dạng.

Lời giải chi tiết

Chọn đáp án D\(\Delta ABC\backsim \Delta DEF\) theo tỉ số đồng dạng \(k\)\(=>\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=k\) (1)\(\Delta MNP\backsim \Delta DEF\) theo tỉ số đồng dạng \(q\)\(=>\frac{MN}{DE}=\frac{NP}{EF}=\frac{MP}{DF}=1\) (2)Từ (1) và (2) \(=>\frac{AB}{MN}=\frac{BC}{NP}=\frac{AC}{MP}=\frac{k}{q}\)=Vậy \(\Delta ABC\backsim \Delta MNP\) theo tỉ số đồng dạng là \(\frac{k}{q}\)

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