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Giải bài 1 trang 96 sách bài tập toán 10 - Chân trời sáng tạo

Cho hình bình hành ABCD có G là trọng tâm của tam giác ABD.

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Đề bài

Cho hình bình hành ABCD có G là trọng tâm của tam giác ABD.

Chứng minh rằng: \(\overrightarrow {AC}  = 3\overrightarrow {AG} \)

Lời giải chi tiết

Gọi O là giao điểm của hai đường chéo trong hình bình hành ABCD

G là trọng tâm của tam giác ABD 🔴nên ta có \(\overrightarrow {AG}  = \frac{2}{3}\overrightarrow {AO} \)

Mà ta có \(\overrightarrow {AO}  = \frac{1}{2}\overrightarrow {AC}  \Rightarrow \overrightarrow {AG}  = \frac{1}{2}.\frac{2}{3}\overrightarrow {AC}  = \frac{1}{3}\overrightarrow {AC} \)Suy ra \(\overrightarrow {AC}  = 3\overrightarrow {AG} \) (đpcm)

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