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Giải bài 4.57 trang 73 sách bài tập toán 11 - Kết nối tri thức với cuộc sống

Cho hình chóp ngũ giác S.ABCDE. Giả sử AB song song với DE.

Tổng hợp đềꦇ 🌄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 ngũ giác S.ABCDE. Giả sử AB song song với DE. a) Xác định giao tuyến của hai mặt phẳng (SAD) và (SBE). b) Xác định giao tuyến của hai mặt phẳng (SAB) và (SDE). c) Giả sử giao tuyến của hai mặt phẳng (SAE) và (SBC) song song với đường thẳng AE. Chứng minh AE//BC

Phương pháp giải - Xem chi tiết

+ Nếu hai mặt phẳng chứa hai đường thẳng song song với nhau thì giao tuyến của chúng (nếu có) song song với hai đường thẳng đó hoặc trùng với một trong hai đường thẳng đó. + Để tìm giao tuyến của hai mặt phẳng, ta đi tìm hai điểm chung thuộc cả hai mặt phẳng đó rồi nối hai điểm chung đó lại ta được giao tuyến cần tìm.

Lời giải chi tiết

a) Gọi O là giao điểm của hai đường thẳng AD và BE thì SO là giao tuyến của hai mặt phẳng (SAD) và (SBE).b) Vì AB//DE nên giao tuyến của hai mặt phẳng (SAB) và (SDE) là đường thẳng m đi qua S và song song với AB.c) Gọi d là giao tuyến của hai mặt phẳng (SAE) và (SBC) thì d//AE. Vì d nằm trong mặt phẳng (SBC) nên AE//(SBC). Mặt phẳng (SBC) song song với đường thẳng AE nằm trong mặt phẳng (ABCDE) nên giao tuyến BC của hai mặt phẳng đó song song với AE.

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