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Giải bài 2 trang 94 sách bài tập toán 10 - Chân trời sáng tạo

Chứng minh rằng với tứ giác ABCD bất kì, ta luôn có:

Tổng hợp đề thi học kì 2 lớp 10 💎tất cả các môn - Chân trờiꦺ sáng tạo

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Đề bài

Chứng minh rằng với tứ giác ABCD bất kì, ta luôn có:

a) \(\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA}  = \overrightarrow 0 \) b) \(\overrightarrow {AB}  - \overrightarrow {AD}  = \overrightarrow {CB}  - \overrightarrow {CD} \)

Phương pháp giải - Xem chi tiết

Sử dụng quy tắc ba điểm \(\overrightarrow {AB}  = \overrightarrow {AM}  + \overrightarrow {MB} \) và phép trừ vectơ \(\overrightarrow {AB}  - \overrightarrow {AC}  = \overrightarrow {CB} \)

Lời giải chi tiết

a) Sử dụng quy tắc ba điểm ta có:\(\begin{array}{l}\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA}  = \left( {\overrightarrow {AB}  + \overrightarrow {BC} } \right) + \left( {\overrightarrow {CD}  + \overrightarrow {DA} } \right)\\ = \overrightarrow {AC}  + \overrightarrow {CA}  = \overrightarrow {AA}  = \overrightarrow 0 \end{array}\) b) \(\begin{array}{l}\overrightarrow {AB}  - \overrightarrow {AD}  = \overrightarrow {DB} ;\overrightarrow {CB}  - \overrightarrow {CD}  = \overrightarrow {DB} \\ \Rightarrow \overrightarrow {AB}  - \overrightarrow {AD}  = \overrightarrow {CB}  - \overrightarrow {CD} \end{array}\)

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