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Giải bài 8 trang 103 SGK Toán 10 tập 1 – Chân trời sáng tạo

Cho tam giác ABC. Bên ngoài tam giác vẽ các hình bình hành ABIJ, BCPQ, CARS

Tổng hợp đề thi học kì 2 lớp 10 tất cả các môn - Cꦺhân trời sáng ♔tạo

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Đề bài

Cho tam giác ABC. Bên ngoài tam giác vẽ các hình bình hành ABIJ, BCPQ, CARS. Chứng minh rằng \(\overrightarrow {RJ}  + \overrightarrow {IQ}  + \overrightarrow💧 {PS}  = \overrightarrow 0 \).

Phương pháp giải - Xem chi tiết

Bước 1: Sử dụng quy tắc ba điểm \(\overrightarrow {AB}  = \overrightarrow {AO}  + \overrightarrow {OB} \)

Bước 2: Xác định các cặp vectơ đối nhau từ các hình bình hành \(\overrightarrow {AB} \) và \(\overrightarrow {CD} \) là hai vectơ đối nhau với ABCD là hình bình hành

Bước 3: Sử dụng tính chất của vectơ đối \(\overrightarrow {AB} \) và \(\overrightarrow {CD} \) là hai vectơ đối nhau thì\(\overrightarrow {AB}  + \overrightarrow {CD}  = \overrightarrow 0 \)

Lời giải chi tiết

  \(\overrightarrow {RJ}  + \overrightarrow {IQ}  + \overrightarrow {PS}  = \left( {\overrightarrow {RA}  + \overrightarrow {AJ} } \right) + \left( {\overrightarrow {IB}  + \overrightarrow {BQ} } \right) + \left( {\overrightarrow {PC}  + \overrightarrow {CS} } \right)\)\( = \left( {\overrightarrow {RA}  + \overrightarrow {CS} } \right) + \left( {\overrightarrow {AJ}  + \overrightarrow {IB} } \right) + \left( {\overrightarrow {BQ}  + \overrightarrow {PC} } \right) = \overrightarrow 0  + \overrightarrow 0  + \overrightarrow 0  = \overrightarrow 0 \)\(\)(đpcm)

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