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Bài 4.6 trang 77 SGK Toán 11 tập 1 - Kết nối tri thức

Cho hình tứ diện ABCD. Trên các cạnh AC, BC, BD lần lượt lấy các điểm M, N, P sao cho AM = CM, BN = CN, BP = 2DP. a) Xác định giao tuyến của đường thẳng CD và mặt phẳng (MNP) b) Xác định giao tuyến của hai mặt phẳng (ACD) và (MNP).

Tổng hợp đề thi học kì🦹 2 lớp 11 tất cả các m♚ôn - Kết nối tri thức

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

Cho hình tứ diện ABCD. Trên các cạnh AC, BC, BD lần lượt lấy các điểm M, N, P sao cho AM = CM, BN = CN, BP = 2DP.

a) Xác định giao tuyến của đường thẳng CD và mặt phẳng (MNP)

b) Xác định giao tuyến của hai mặt phẳng (ACD) và (MNP).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Để xác định giao tuyến của hai mặt phẳng, ta tìm hai điểm chung thuộc cả hai mặt phẳng đó

Lời giải chi tiết

a) Xét trên mp(BCD): NP cắt CD tại I

I thuộc NP suy ra I nằm trên mp(MNP)

Suy ra giao điểm của CD và mp(MNP) là I

b) Ta có I, M đều thuộc mp(ACD) suy ra IM nằm trên mp(ACD)

I, M đều thuộc mp(MNP) suy ra IM nằm trên mp(MNP)

Do đó, IM là giao tuyến của 2 mp(ACD) và mp(MNP) hay EM là giao tuyến của 2 mp(ACD) và mp(MNP).

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