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Giải bài 4 trang 90 vở thực hành Toán 8 tập 2

Cho các điểm A, B, C, D, E, F như Hình 9.8. Biết rằng DE // AB, EF // BC, DE = 4cm, AB = 6cm. Chứng minh rằng ΔAEF ∽ ΔECD và tính tỉ số đồng dạng

💦Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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

ꦅCho các điểm A, B, C, D, E, F như Hình 9.8. Biết rằng DE // AB, EF // BC, DE = 4cm, AB = 6cm. Chứng minh rằng ΔAEF ∽ ΔECD và tính tỉ số đồng dạng

 

Phương pháp giải - Xem chi tiết

Áp dụng tính chất hai đường thẳng song song => Các cặp góc bằng nhau => Hai tam giác đồng dạng, ta có tỉ số đồng dạng

Lời giải chi tiết

Do BFED là hình bình hành nên BF = DE = 4 cm.Do đó AF = AB – BF = 2cm.Hai tam giác AEF và ECD có: $\widehat{AEF}=\widehat{ECD},\widehat{EAF}=\widehat{CED}$ (các cặp góc đồng vị).Do đó $\Delta AEF\backsim \Delta ECD$ (g.g) với tỉ số đồng dạng bằng $\frac{AF}{ED}=\frac{2}{4}=\frac{1}{2}$.

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