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Câu 39 trang 68 SGK Hình học 11 Nâng cao

Cho hình chóp cụt ABC.A’B’C’ có đáy lớn ABC và các cạnh bên AA’, BB’, CC’. Gọi M, N, P lần lượt là trung điểm của các cạnh AB, BC, CA và M’, N’, P’ lần lượt là trung điểm của các cạnh A’B’, B’C’, C’A’. Chứng minh MNP.M’N’P’ là hình chóp cụt
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Đề bài

 Cho hình chóp cụt ABC.A’B’C’ có đáy lớn ABC và các cạnh bên AA’, BB’, CC’. Gọi M, N, P lần lượt là trung điểm của các cạnh AB, BC, CA và M’, N’, P’ lần lượt là trung điểm của các cạnh A’B’, B’C’, C’A’. Chứng minh MNP.M’N’P’ là hình chóp cụt

Lời giải chi tiết

 

Gọi S là giao điểm các cạnh bên AA’, BB’, CC’của hình chóp cụt.Do A’B’ // AB và M’, M lần lượt là trung điểm của A’B’, AB nên MM’ đi qua S.Tương tự NN’, PP’ cùng đi qua S.Vậy MM’, NN’, PP’ đồng quy tại S.Ta có (M’N’P’) // (MNP) nên MNP.M’N’P’ là hình chóp cụt.

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