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Giải Bài 9.18 trang 55 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

Cho tam giác ABC với M là trung điểm của BC. Lấy điểm N sao cho C là trung điểm của đoạn thẳng BN. Lấy điểm P sao cho M là trung điểm của đoạn thẳng AP. Chứng minh đường thẳng AC đi qua trung điểm của PN, đường thẳng PC đi qua trung điểm của AN.

✤Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

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

Cho tam giác ABC với M là trung điểm của BC. Lấy điểm N sao cho C là trung điểm của đoạn thẳng BN. Lấy điểm P sao cho M là trung điểm của đoạn thẳng AP. Chứng minh đường thẳng AC đi qua trung điểm của PN, đường thẳng PC đi qua trung điểm của AN.

Phương pháp giải - Xem chi tiết

Chứng minh CN = 2CM Từ đó suy ra: C là trọng tâm tam giác APN

Lời giải chi tiết

Ta có: M là trung điểm BC nên BM = CM = \(\dfrac{1}{2}BC\) \( \Rightarrow BC = 2CM\) C là trung điểm BN nên BC = CN \( \Rightarrow CN = 2CM\) Xét tam giác ANP có NM là đường trung tuyến Mà: CN = 2CM (cmt) \( \Rightarrow \) C là trọng tâm tam giác ANP \( \Rightarrow \) AC, PC là hai tiếp tuyến của tam giác đó \( \Rightarrow \) AC đi qua trung điểm của PN     PC đi qua trung điểm của AN.

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