Cho lăng trụ tam giác ABC.ABC.Gọi I,I theo thứ tự là trung điểm của các cạnh BC,BC
a. Chứng minh AI//AI
b. Tìm giao điểm của đường thẳng IA với mặt phẳng (ABC)
c. Chứng minh rằng giao tuyến của hai mặt phẳng (ABC),(BAC) song song với cạnh AC

a. Ta có II//AA
II=AA
AIIA là hình bình hành, suy ra AI//AI
b. Gọi D=AIAI
DAI(1)
DAID(ABC)(2)
Từ (1),(2) suy ra :
DAI(ABC)
c. Gọi E=ABAB
E(ABC)E(BAC)(3)
F=BCBC
F(BAC)F(ABC)(4)
Từ (3),(4) suy ra EF=(ABC)(BAC)
Trong ΔBAC,EF là đường trung bình, vậy EF//AC

Thẻ

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