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Câu 42 trang 74 SGK Hình học 11 Nâng cao

Tam giác ABC có hình chiếu song song là tam giác A’B’C’. Chứng minh rằng trọng tâm tam giác ABC có hình chiếu song song là trọng tâm tam giác A’B’C’
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Đề bài

Tam giác ABC có hình chiếu song song là tam giác A’B’C’. Chứng minh rằng trọng tâm tam giác ABC có hình chiếu song song là trọng tâm tam giác A’B’C’

Lời giải chi tiết

 

Gọi G là trọng tâm ∆ABC, M là trung điểm BCG’, M’ là hình chiếu song song của G và M.Ta có M’ là trung điểm B’C’ và \({{A'G'} \over {G'M'}} = {{AG} \over {GM}} = 2\)\(⇒\) G’ là trọng tâm ∆A’B’C’.

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