In cube ABCDA1B1C1D1, pick a plane parallel to plane A1BC1 and passing through the three vertices of the cube.
| April 19, 2021 | education
To find a plane that will be parallel to the given one, we will have to build a triangle on it, the sides of which will be parallel to the given one (according to the condition, the plane must pass through the three vertices of the cube).
To solve the problem, it is necessary that the sides are located on the parallel faces of the cube.
The A1C1 side is located on the A1B1C1D1 edge. This face will be parallel to ABCD. This means that the parallel side will be AC.
The A1B side is located on the АА1В1В edge. This facet will be parallel to the facet DD1C1C. Hence, the parallel side will be D1C.
The ВС1 side is located on the В1BC1С edge. This face will be parallel to face DD1A1A. Hence, the parallel side will be AD1.
We get a parallel plane ACD1.
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