Similarity proof refers to the method of deducing conclusions through similar properties, theorems or formulas when solving mathematical problems. These methods can help us better understand and master mathematical knowledge and improve our ability to solve problems.
Analogy is a common method to prove similarity, and it is a method to draw new conclusions by comparing two or more similar things. In mathematical proof, we can find similar new problems by observing the solutions of known problems, and then use the solutions of known problems to solve new problems.
Reduction to absurdity, reduction to absurdity is a method to prove that a proposition is true by assuming that it is false and then deducing a contradiction. In mathematical proof, we can prove that a conclusion must be true by assuming that it is not true and then deducing a result that contradicts the known conditions.
The difference between similarity and consistency
1, Definition: Similarity If the shapes of two graphs are exactly the same, then we can say that they are similar. In other words, two graphs are said to be similar if they can be translated, rotated and flipped.
If two figures are not only the same shape, but also the same size, then we say they are congruent. In other words, if two graphs can be translated, rotated, flipped and scaled to get each other, and these operations will not change the size of the graphs, then we say that they are congruent.
2. Transformation: Similarity can be achieved by scaling, rotating, flipping and other proportional transformations. Congruence relation can be realized by rigid body transformation such as translation, rotation and turnover.
3. Features: Similar objects or figures have the same shape, but their sizes may be different, but they just maintain a relative proportional relationship. The same object or figure is exactly the same in shape and size, and there is no difference.
4. Representation: Similarity is usually expressed by proportion, that is, the ratio of the lengths of the corresponding parts of two objects or figures is equal. Congruence is usually represented by the symbol ≦.