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Giải bài 3 trang 92 SGK Toán 10 tập 1 – Cánh diều

Cho tam giác ABC có M, N, P lần lượt là trung điểm của BC, CA, AB. Chứng minh:

📖Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Cho tam giác ABC có M, N, P lần lượt là trung điểm của BC, CA, AB. Chứng minh: a) \(\overrightarrow {AP}  + \frac{1}{2}\overrightarrow {BC}  = \overrightarrow {AN} \) b) \(\overrightarrow {BC}  + 2\overrightarrow {MP}  = \overrightarrow {BA} \)

Phương pháp giải - Xem chi tiết

Quy tắc cộng:  \(\overrightarrow {AP}  + \overrightarrow {PN}  = \overrightarrow {AN} \) a) Chỉ ra \(\frac{1}{2}\overrightarrow {BC}  = \overrightarrow {PN} \) b) Chỉ ra \(2\overrightarrow {MP}  = \overrightarrow {CA} \).

Lời giải chi tiết

a) Ta có: \(\overrightarrow {BC} ,\overrightarrow {PN} \) là hai vecto cùng hướng và \(\frac{1}{2}\left| {\overrightarrow {BC} } \right| = \left| {\overrightarrow {PN} } \right|\)\( \Rightarrow \frac{1}{2}\overrightarrow {BC}  = \overrightarrow {PN} \)\( \Rightarrow \overrightarrow {AP}  + \frac{1}{2}\overrightarrow {BC}  = \overrightarrow {AP}  + \overrightarrow {PN}  = \overrightarrow {AN} \)b) Ta có: \(\overrightarrow {MP} ,\overrightarrow {CA} \) là hai vecto cùng hướng và \(2\left| {\overrightarrow {MP} } \right| = \left| {\overrightarrow {CA} } \right|\)\( \Rightarrow 2\overrightarrow {MP}  = \overrightarrow {CA} \)\( \Rightarrow \overrightarrow {BC}  + 2\overrightarrow {MP}  = \overrightarrow {BC}  + \overrightarrow {CA}  = \overrightarrow {BA} \)

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Ph/hs Tham Gia Nhóm Để Cập Nhật Điểm Thi, Điểm Chuẩn Miễn Phí

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