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Giải bài 4.9 trang 50 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Cho tứ giác ABCD

Tổng hợpꦰ đề thi học kì 2 lớp 10 tất cả cáꦐc môn - Kết nối tri thức

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Đề bài

Cho tứ giác \(ABCD.\) a) Chứng minh rằng \(\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA}  = \overrightarrow 0 .\) b) Chứng minh rằng \(\overrightarrow {AB}  + \overrightarrow {CD}  = \overrightarrow {AD}  + \overrightarrow {CB} .\)

Lời giải chi tiết

a) \(\overrightarrow {AB}  + \overrightarrow {BC}  + \overrightarrow {CD}  + \overrightarrow {DA} \) \(\begin{array}{l} = \left( {\overrightarrow {AB}  + \overrightarrow {BC} } \right) + \left( {\overrightarrow {CD}  + \overrightarrow {DA} } \right)\\ = \overrightarrow {AC}  + \overrightarrow {CA}  = \overrightarrow 0 \end{array}\) b) Biến đổi vế trái: \(\overrightarrow {AB}  + \overrightarrow {CD} \) \( = \left( {\overrightarrow {AD}  + \overrightarrow {DB} } \right) + \left( {\overrightarrow {CB}  + \overrightarrow {BD} } \right)\) \( = \overrightarrow {AD}  + \overrightarrow {CB}  + \left( {\overrightarrow {DB}  + \overrightarrow {BD} } \right)\) \( = \overrightarrow {AD}  + \overrightarrow {CB} \) (đpcm)

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