1. In the case of isosceles triangle, the key point is the relationship between equilateral and equilateral. You can solve the problem from the midpoint of the bottom and use the midline of the isosceles triangle to solve the problem. See section 2.

2. 1 times the midline length to construct a parallelogram.

Let's prove the relationship between the center line and this side. For example, if you find something vertical, you can find a breakthrough in the process of proving or solving problems.

3 Use the nature of the center of gravity to solve the problem.

3. This is rather general and complicated. One can connect diagonal lines in parallel, and the other can be divided into small triangles to deal with.

4. We mainly use the equality of opposite and diagonal sides to construct similarity or congruence, and find the breakthrough of solving problems. Making auxiliary lines when you are not in a hurry will only increase the difficulty of solving problems.

Simple questions can be done with reference to 4, and difficult questions can be solved by rotating some triangles with equal adjacent sides.

6. Such problems are rare, and congruence is generally enough.

You don't have to make auxiliary lines for every question, and you don't have to follow the rules to make auxiliary lines. If you can't do it or prove it, you might as well start from the conclusion, find the conclusion that needs to be proved and make the necessary auxiliary lines. This is my opinion.