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Bài 4.29 trang 124 SGK Toán 11 tập 1 - Cùng khám phá

Cho hình chóp S.ABCD có đáy là hình thang ABCD với AD là đáy lớn. Gọi M, E lần lượt là trung điểm của CD, SB.
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Đề bài

Cho hình chóp S.ABCD có đáy là hình thang ABCD với AD là đáy lớn. Gọi M, E lần lượt là trung điểm của CD, SB. a) Xác định giao tuyến của (SAD) và (SBC). b) Chứng minh rằng EM // (SAD).

Phương pháp giải - Xem chi tiết

a) (P) // (Q), a nằm trong (P) và b nằm trong (Q) song song với nhau, d là giao tuyến của (P) và (Q) thì a // b // d. b) Nếu đường thẳng d không nằm trong (P) song song với đường thẳng a nằm trong (P) thì d song song với (P).

Lời giải chi tiết

a) (SAD) và (SBC) có chung điểm S, có chứa lần lượt 2 đường thẳng AD và BC song song với nhau nên giao tuyến của (SAD) và (SBC) là đường thẳng đi qua S, song song với AD, BC.b) Trong (ABCD), gọi F là giao điểm của BM và ADTa có AF // BC nên \(\frac{{MF}}{{BM}} = \frac{{DM}}{{CM}} = 1 \Rightarrow MF = BM\)Xét tam giác SBF có E, M lần lượt là trung điểm của SB, BF nên EM // SFF thuộc AD nên F thuộc (SAD) hay SF nằm trong (SAD)Vậy EM // (SAD).

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