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Giải bài 4.15 trang 59 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình chóp S.ABCD có đáy ABCD là hình thang (AB//CD). Gọi M, N lần lượt là các điểm thuộc các cạnh SA, SD.

🐼Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Cho hình chóp S.ABCD có đáy ABCD là hình thang (AB//CD). Gọi M, N lần lượt là các điểm thuộc các cạnh SA, SD. a) Xác định giao tuyến d của hai mặt phẳng (MCD) và (NAB). b) Chứng minh rằng d // AB.

Phương pháp giải - Xem chi tiết

Dựa vào định lý về 3 đường giao tuyến của 3 mặt phẳng: Nếu có 2 giao tuyến của song song với nhau thì giao tuyến thứ 3 cũng song song với 2 giao tuyến đó. Còn nếu có 2 giao tuyến cắt nhau thì 3 giao tuyến đó đồng quy.

Lời giải chi tiết

a) Xét ba mặt phẳng (MCD), (NAB) và (ABCD)CD là giao tuyến của (MCD) và (ABCD)AB là giao tuyến của (NAB) và (ABCD)Mà AB//CD nên giao tuyến d của (MCD) và (NAB) cũng song song với AB và CD.Gọi P là giao điểm của MD và NA trên mặt phẳng (SAD), vậy P là một điểm chung của (MCD) và (NAB). Vậy giao tuyến d sẽ là đường thẳng qua P, song song với AB, CD.b) Vậy d // AB.

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