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Giải bài 2 trang 108 SGK Toán 8 tập 1 - Cánh diều

Cho tam giác ABC có

💦Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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

Cho tam giác ABC có hai đường trung tuyến BM và CN cắt nhau tại G. Gọi P và Q lần lượt là trung điểm của GB và GC. Chứng minh tứ giác PQMN là hình bình hành.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

𒊎Chứng minh tứ giác PQMN có hai đường chéo cắt nhau tại trung điểm của mỗi đường

Lời giải chi tiết

\(\Delta ABC\) có hai đường trung tuyến BM và CN cắt nhau tại G.Suy ra G là trọng tâm của tam giác.\( \Rightarrow BG = \dfrac{2}{3}BM;GM = \dfrac{1}{3}BM\left( 1 \right)\)Mà: \(PG = \dfrac{1}{2}BG = \dfrac{1}{2}.\dfrac{2}{3}BM = \dfrac{1}{3}BM\left( 2 \right)\)Từ (1), (2) suy ra GM = PGChứng minh tương tự ta cũng có QG = GNTứ giác PQMN có hai đường chéo QN và PM cắt nhau tại trung điểm mỗi đường nên tứ giác PQMN là hình bình hành

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Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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