Hướng dẫn giải Bài 6 (Trang 92 SGK Toán Hình học 11)

Cho hình tứ diệnABCD. Gọi G là trọng âm của tam giác ABC. Chứng minh rằng: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>D</mi><mi>A</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mn>3</mn><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover></math> Giải: G là trọng tâm tam giác ABC nên <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>G</mi><mi>A</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></math>. Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>D</mi><mi>A</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mfenced><mrow><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>A</mi></mrow><mo>→</mo></mover></mrow></mfenced><mo>+</mo><mfenced><mrow><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>B</mi></mrow><mo>→</mo></mover></mrow></mfenced><mo>+</mo><mfenced><mrow><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>C</mi></mrow><mo>→</mo></mover></mrow></mfenced><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mn>3</mn><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover><mo>+</mo><mo>(</mo><mover><mrow><mi>G</mi><mi>A</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>G</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>)</mo><mo>=</mo><mn>3</mn><mover><mrow><mi>D</mi><mi>G</mi></mrow><mo>→</mo></mover></math>

Giải bài tập 6 (SGK Toán 11, trang 92, Hình học)

GV:

GV colearn

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