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Giải bài 2 trang 97 sách bài tập toán 10 - Chân trời sáng tạo

Gọi AM là trung tuyến của tam giác ABC và D là trung điểm của đoạn AM. Chứng minh rằng:

Tổng hợp đề thi học kì 2 lớp 10 tấ𒁏t cả các môn - Chân trời sáng tạo

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Đề bài

Gọi AM  là trung tuyến của tam giác ABC và D là trung điểm của đoạn AM. Chứng minh rằng:

a) \(2\overrightarrow {DA}  + \overrightarrow {DB}  + \overrightarrow {DC}  = \overrightarrow 0 \)

b)  \(2\overrightarrow {OA}  + \overrightarrow {OB}  + \overrightarrow {OC}  = 4\overrightarrow {OD} \)        với O là điểm tùy ý

Phương pháp giải - Xem chi tiết

Sử dụng tính chất trung điểm \(\overrightarrow {MA}  + \overrightarrow {MB}  = 2\overrightarrow {MI} \) với I là trung điểm của AB

Lời giải chi tiết

a) AM  là trung tuyến của tam giác ABC, suy ra M là trung điểm của BC

\(2\overrightarrow {DA}  + \overrightarrow {DB}  + \overrightarrow {DC}  = 2\overrightarrow {DA}  + \left( {\overrightarrow {DB}  + \overrightarrow {DC} } \right) \\= 2\overrightarrow {DA}  + 2\overrightarrow {DM}  = 2\left( {\overrightarrow {DA}  + \overrightarrow {DM} } \right) = \overrightarrow 0 \)

(D là trung điểm của AM nên \(\overrightarrow {DA}  + \overrighta🌟rrow {DM}  = \o𒆙verrightarrow 0 \))

b)\(\begin{array}{l}2\overrightarrow {OA}  + \overrightarrow {OB}  + \overrightarrow {OC}  = 2\overrightarrow {OA}  + \left( {\overrightarrow {OB}  + \overrightarrow {OC} } \right) = 2\overrightarrow {OA}  + 2\overrightarrow {OM} \\ = 2\left( {\overrightarrow {OA}  + \overrightarrow {OM} } \right) = 2.2\overrightarrow {OD}  = 4\overrightarrow {OD} \end{array}\) 

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

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