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Giải bài 2 trang 76 SGK Toán 8 tập 2– Chân trời sáng tạo

Quan sát Hình 9. a) Chứng minh rằng

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

Quan sát Hình 9. a) Chứng minh rằng \(\Delta DEF\backsim\Delta HDF\). b) Chứng minh rằng \(D{F^2} = FH.FE\). c) Biết \(EF = 15cm,FH = 5,4cm\). Tính độ dài đoạn thẳng \(DF\).

 

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Nếu một tam giác vuông này có một góc nhọn bằng góc nhọn của tam giác vuông kia thì hai tam giác vuông đó đồng dạng với nhau.

Lời giải chi tiết

a)  Xét \(\Delta DEF\) và \(\Delta HDF\) có: \(\widehat F\) chung \(\widehat {EDF} = \widehat {DHF} = 90^\circ \) Do đó, \(\Delta DEF\backsim\Delta HDF\) (g.g) b) Vì \(\Delta DEF\backsim\Delta HDF\) nên \(\frac{{DF}}{{HF}} = \frac{{FE}}{{DF}}\) (các cặp cạnh tương ứng có cùng tỉ lệ) \( \Rightarrow D{F^2} = FH.FE\). c) Theo câu b ta có: \(D{F^2} = FH.FE\) Thay số, \(D{F^2} = 5,4.15 = 81 \Rightarrow DF = \sqrt {81}  = 9cm\) Vậy \(DF = 9cm\).

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