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Giải bài 37 trang 92 SBT toán 10 - Cánh diều

Cho tứ giác ABCD, O là trung điểm của AB. Chứng minh \(\overrightarrow {OC} + \overrightarrow {OD} = \overrightarrow {AC} + \overrightarrow {BD} \)(*)

Tổng hợp đề thi học kඣì 2 lớp 10 tất cả các m🤪ôn - Cánh diều

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Đề bài

Cho tứ giác ABCD, O là trung điểm của AB. Chứng minh \(\overrightarrow {OC}  + \overrig🃏htarrow {OD}  = \overrightarrow {AC}  + \overrightarrow {B𓆉D} \)(*)

Phương pháp giải - Xem chi tiết

Sử dụng quy tắc 3 điểm (chọn O là điểm trung gian) và trung điểm của🌺 đoạn thẳng để biến đổi một vế của (*) bằng vế còn lại

Lời giải chi tiết

Do O là trung điểm của AB nên \(\overrightarrow {OA}  + \overrightarrow {OB}  = \overಌrightarrow 0 \)

Biến đổi vế phải của (*) ta có:\(\overrightarrow {AC}  + \overrightarrow {BD}  = \overrightarrow {OC}  - \overrightarrow {OA}  + \overrightarrow {OD}  - \overrightarrow {OB}  = (\overrightarrow {OC}  + \overrightarrow {OD} ) - (\overrightarrow {OA}  + \overrightarrow {OB} )\)\( = (\overrightarrow {OC}  + \overrightarrow {OD} ) - \overrightarrow 0  = \overrightarrow {OC}  + \overrightarrow {OD} \) = Vế trái (*) (ĐPCM)

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