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Giải bài 4 trang 93 SGK Toán 10 tập 1 – Chân trời sáng tạo

Cho hình bình hành ABCD có O là giao điểm hai đường chéo. Chứng minh rằng:

Tổng hợp đề thi học kì 2 lớp 10 tất cả cá🅺c môn - Chân trời sáng tạo

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Đề bài

Cho hình bình hành ABCD có O là giao điểm hai đường chéo. Chứng minh rằng:

a) \(\overrightarrow {OA}  - \overrightarrow {OB}  = \overrightarrow {OD}  - \overrightarrow {OC;} \)                                   

b) \(\overrightarrow {OA}  - \overrightarrow {OB}  + \overrightarrow {DC}  = \overrightarrow 0 \)

Phương pháp giải - Xem chi tiết

Vận dụng quy tắc hiệu: \( \overrightarrow {OA} - \overrightarrow {OB} = \overrightarrow {BA}  \)

Lời giải chi tiết

a) \(\overrightarrow {OA}  - \overrightarrow {OB}  = \overrightarrow {BA} \)\(\overrightarrow {OD}  - \overrightarrow {OC}  = \overrightarrow {CD} \)

Do ABCD là hìn🌠h bình hành nên \(\overrightarrow {BA}  = \overrightarrow {CD} \)

Suy ra, \(\overrightarrow {OA}  - \overrightarrow {OB}  = \overrightarrow {OD}  - \overrightarrow {OC} \)b)  \(\overrightarrow {OA}  - \overrightarrow {OB}  + \overrightarrow {DC}  = (\overrightarrow {OD}  - \overrightarrow {OC})  + \overrightarrow {DC}  \\= \overrightarrow {CD}  + \overrightarrow {DC} = \overrightarrow {CC} = \overrightarrow 0 \)

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