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Giải bài 14 trang 51 sách bài tập toán 8 - Chân trời sáng tạo tập 2

Cho Hình 10, tính độ dài x, y.

🍎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

Cho Hình 10, tính độ dài x, y.

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về tính chất của đường trung bình của hình thang: Đường thẳng đi qua trung điểm một cạnh bên của hình thang và song song với hai đáy thì đi qua trung điểm của cạnh bên thứ hai và được gọi là đường trung bình của hình thang. Đường trung bình của hình thang song song với hai đáy và bằng nửa tổng hai đáy.

Lời giải chi tiết

Vì EF//DC (cùng vuông góc với AD) nên tứ giác EFCD là hình thang.Hình thang EFCD có: H là trung điểm của FC, GH//EF//DC (cùng vuông góc với AD) nên G là trung điểm của ED. Suy ra, GH là đường trung bình của hình thang EFCD. Suy ra: \(GH = \frac{{FE + DC}}{2} = \frac{{10 + 14}}{2} = 12\) hay \(y = 12\)Vì AB//GH (cùng vuông góc với AD) nên tứ giác ABHG là hình thang.Hình thang ABHG có: F là trung điểm của BH, AB//EF//GH (cùng vuông góc với AD) nên E là trung điểm của AG. Suy ra, EF là đường trung bình của hình thang ABHG. Suy ra: \({\rm{EF}} = \frac{{AB + GH}}{2}\), hay \(10 = \frac{{x + 12}}{2}\), suy ra \(x = 8\).

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