But notice that the plane is wireless, while the quadrilateral is finite, and the parallelogram is in the same plane before and after extension.
Just as a straight line is infinite and a line segment is finite, the straight line extended by the line segment remains unchanged.
So we often use two points to represent straight lines, such as straight lines AB, A and B on a straight line.
Similarly, a plane can also be represented by more than three points, such as plane ABCD, where A, B, C and D are all in the plane.
Of course, these four points are also the vertices of the quadrilateral ABCD.
This plane represents the plane of quadrilateral ABCD.
If the point EFG is in the quadrilateral ABCD, the triangle EFG and the quadrilateral ABCD*** plane,
In other words, the ABCD plane and the EFG plane are one plane.
Just like two line segments.
This explains your understanding of two axioms.
Heteroplane straight line
The first statement is wrong,
For example, the cuboid ABCD-a' b' c' d'
AB is on the ABCD plane,
A' b' in plane b' c' d',
They are in different planes, but they are parallel, not straight lines in different planes.
It is different in any plane, that is, there is no plane, so that two straight lines are in this plane at the same time.
For example, the horizontal edge on the front and the vertical edge on the back of a cuboid.
If you don't understand, please ask.
If my answer solves your problem, please adopt it.