1, definition method and vertical method: if two planes have nothing in common, they are parallel. This method can usually be realized by proving that straight lines on two planes have no intersection. If a straight line in one plane is perpendicular to the other plane, the two planes are parallel. This method needs to prove that this straight line is perpendicular to another plane and that this straight line is not in another plane.

2. Theorem method: If two intersecting straight lines in a plane are parallel to another plane, then the two planes are parallel. This method needs to prove that these two intersecting straight lines are parallel to another plane, and the straight lines in one plane do not intersect with the other plane.

3. Reduction to absurdity: If a straight line in one plane intersects another plane, the two planes are not parallel. This method needs to prove that this straight line intersects another plane by reduction to absurdity, thus overthrowing the hypothesis.

4. Decision theorem method: If two intersecting straight lines in one plane are parallel to the intersection line of another plane, the two planes are parallel. This method needs to prove that the intersecting lines of these two intersecting lines are parallel to each other, and that the lines in one plane do not intersect with the intersecting lines in the other plane.

Prove the advantages of two parallel planes

1, simplifying the geometric problem: when two planes are parallel, the positional relationship between them is relatively simple, and the geometric problem can be simplified by using parallelism. For example, plane parallelism can be used to prove that two triangles are similar or congruent, thus simplifying some problems of proof and calculation.

2. Supplementary proof methods: There are many ways to prove that two planes are parallel, and the most suitable method can be selected according to the specific situation. These methods can be used in various geometric problems, which increases the diversity of solving methods and skills.

3. Deepen the understanding of geometric concepts: proving that two planes are parallel requires understanding geometric concepts and properties, such as the definition of planes, the definition of parallelism, axioms and theorems. By proving that the two planes are parallel, we can understand the essence and application of these concepts and properties more deeply.

4. Improve mathematical literacy: proving that two planes are parallel requires rigorous mathematical thinking and rigorous logical reasoning, which is helpful to improve mathematical literacy. By proving that the two planes are parallel, we can cultivate the ability of logical reasoning and mathematical analysis, thus solving other mathematical problems better.