Do you know that?/You know what? Do you know that?/You know what? You made a big mistake in this proof. For proving four points, you can't prove completeness just two or four times.

Let me give you a counterexample. If E is on the straight line A 1B 1, then according to your proof method, is E also on the plane of F***, on the plane of D 1? However, at this time, EF crosses CD 1 by translating to DCC 1D 1 plane, that is to say, EF and CD 1 are out of the plane at this time, and the four points are not * * * plane.

Even if you use your proof method to prove four points, it can only show that every two points can be connected by a line segment.

Then I'll talk about my proof method. Generally, it can be proved that four points * * * can be used in three ways: 1) Two straight lines are parallel; 2) Two straight lines intersect; 3) Three of the points are on the plane, and the other point is proved to be on this plane.

This question is easier to use the first one.

Connect A 1B and prove that A 1BCD 1 is a parallelogram = >; a 1B//d 1C- 1；

E and f are the midpoint of straight lines AB and AA 1 respectively = & gtEF is the center line of triangle A 1AB = >; EF//a 1 b-2；

According to the two conditions of 1 2, ef//d1c = >; E, f, c, D 1*** plane.

Note: You can also try the latter two methods. Very interesting. In fact, your original proof method may come from some assumptions, so try to prove it according to theorems and axioms when you usually prove it. Of course, in order to deepen understanding, you need to draw your own pictures, and sometimes you can use math software such as MATLAB and Maple.