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Giải bài 6 trang 87 SGK Toán 10 tập 1 – Cánh diều

Cho ABCD là hình bình hành. Chứng minh

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

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Đề bài

Cho ABCD là hình bình hành. Chứng minh \(\overrightarrow {MB}  - \overrightarrow {MA}  = \overrightarrow {MC}  - \overrightarrow {MD} \) với mỗi điểm M trong mặt phẳng.

Phương pháp giải - Xem chi tiết

Sử dụng vecto đối đưa về tổng hai vecto.

Lời giải chi tiết

Ta có: \(\overrightarrow {AM}  =  - \overrightarrow {MA} ,\;\overrightarrow {DM}  =  - \overrightarrow {MD} \)\( \Rightarrow \overrightarrow {MB}  - \overrightarrow {MA}  = \overrightarrow {MB}  + \overrightarrow {AM}  = \overrightarrow {AM}  + \overrightarrow {MB}  = \overrightarrow {AB} \)Tương tự ta có: \(\overrightarrow {MC}  - \overrightarrow {MD}  = \overrightarrow {MC}  + \overrightarrow {DM}  = \overrightarrow {DM}  + \overrightarrow {MC}  = \overrightarrow {DC} \)Mà \(\overrightarrow {AB}  = \overrightarrow {DC} \)(do ABCD là hình bình hành)\( \Rightarrow \overrightarrow {MB}  - \overrightarrow {MA}  = \overrightarrow {MC}  - \overrightarrow {MD} \) (đpcm)

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