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Câu 28 trang 60 SGK Hình học 11 Nâng cao

Cho hình chóp S.ABCD có đáy là hình bình hành. Xác định thiết diện của hình chóp khi cắt bởi mặt phẳng đi qua trung điểm M của cạnh AB, song song với BD và SA
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Đề bài

Cho hình chóp S.ABCD có đáy là hình bình hành. Xác định thiết diện của hình chóp khi cắt bởi mặt phẳng đi qua trung điểm M của cạnh AB, song song với BD và SA

Lời giải chi tiết

 


Gọi (β) là mặt phẳng qua M và song song với BD, SA.BD // (β) nên (β) cắt mp(ABCD) theo giao tuyến MN // BD (N \(\in\) AD).SA // (β) nên (β) cắt mp(SAB) theo giao tuyến MP // SA (P \(\in\) SB).(β) cắt mp(SAD) theo giao tuyến NQ // SA (Q \(\in\) SD ).Gọi {I} = MN ∩ AC.(β) cắt mp(SAC) theo giao tuyến IK // SA (K \(\in\) SC)Thiết diện cần tìm là ngũ giác MNQKP.

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