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Giải bài 9 trang 126 vở thực hành Toán 8 tập 2

Cho tam giác ABC. Các đường trung tuyến AF, BE và CD cắt nhau tại G. Gọi I, K theo thứ tự là trung điểm của BG và CG

꧙Tổng 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

𓆉Cho tam giác ABC. Các đường trung tuyến AF, BE và CD cắt nhau tại G. Gọi I, K theo thứ tự là trung điểm của BG và CG

a) Chứng minh rằng tứ giác DEKI là hình bình hành

💃b) Biết AF = 6cm. Tính độ dài các đoạn thẳng DI và EK

Phương pháp giải - Xem chi tiết

a) Chứng minh tứ giác DEKI có các cặp cạnh đối song song với nhau nên DEKI là hình bình hành. b) Sử dụng tính chất trọng tâm của tam giác.

Lời giải chi tiết

a) Do DE là đường trung bình của tam giác ABC nên DE // BC và DE = \(\frac{{BC}}{2}\).Tương tự, IK là đường trung bình của tam giác GBC nên IK // BC và IK = \(\frac{{BC}}{2}\).Từ hai kết quả trên, suy ra DE // IK và DE = IK. Tứ giác DEKI có hai cạnh đối diện song song và bằng nhau nên là hình bình hành.b) Vì G là trọng tâm của tam giác ABC nên AG = \(\frac{{2AF}}{3}\) = 4cm.Mặt khác EF là đường trung bình của tam giác CAG nên EK = \(\frac{{AG}}{2}\) = 2cm.Chứng minh tương tự ta cũng có DI là đường trung bình của tam giác BAG.Từ đó suy ra DI = EK = 2cm.

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