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Giải bài 3 trang 61 vở thực hành Toán 8

Chứng minh rằng các trung điểm của bốn cạnh trong một hình chữ nhật là các đỉnh của hình thoi

🌊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

♒Chứng minh rằng các trung điểm của bốn cạnh trong một hình chữ nhật là các đỉnh của hình thoi

Phương pháp giải - Xem chi tiết

- Sử dụng tính chất của đường trung bình. - Sử dụng dấu hiệu nhận biết hình bình hành, hình thoi.

Lời giải chi tiết

🅰(H.3.34). Ta có \(AE{\rm{ }} = \;EB,\;AH{\rm{ }} = \;HD\; \Rightarrow \;HE{\rm{ }}//\;BD,\;HE{\rm{ }} = \;\frac{1}{2}BD\).

𓂃Tương tự \(GF{\rm{ }}//\;BD,{\rm{ }}GF{\rm{ }} = \;\;\frac{1}{2}BD,\;EF{\rm{ }}//\;AC,\;EF{\rm{ }} = \;\frac{1}{2}AC\).

Suy ra HE // GF, HE = GF, do đó HEFG là hình bình hành.

ꦏTứ giác ABCD là hình chữ nhật nên AC = BD ⇒ HE = GF = EF = HG ⇒ HEFG là hình thoi.

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