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When math problems are said without any conditions, can they be used as auxiliary lines? If you don't add it
Without any conditions, that is to say, you can't add any conditions directly obtained from known conditions.

If it is a new condition that can be proved from a known condition, it must be proved.

If you can't prove it from the existing conditions, that is, measure it with a ruler, you can't use it if you feel this way.

Auxiliary line refers to the line that actually exists in the picture without drawing the topic itself (it does not depend on the drawing method of specific size, but the abstract drawing method of the topic), which is helpful to solve the problem.

Since pictures exist objectively, they belong to the existing conditions of the topic. Does not belong to the condition of adding.

For example, a triangle should be proved to be an isosceles triangle.

The condition of the topic does not directly give the equality of edges and angles, so we can't use rulers and protractors to measure and say equality. This is the condition. Conditions.

But for yesterday's convenience, draw a center line. Although the original picture does not have this center line. But any triangle has three median lines. So the existence of this middle line means that when it is a triangle, it contains conditions, but it is not drawn. Therefore, drawing this middle line as an auxiliary line is not a condition to be added, but an existing condition, so we should make full use of the existing conditions.