For junior high school students who are new to geometry, they often feel at a loss and have no clue. How to solve a seemingly complex geometric problem by obtaining a concise and clear solution is an important problem faced by geometric problems, and adding auxiliary lines appropriately is a good way to solve this problem. Based on my personal experience, I talk about the practice of commonly used auxiliary lines.

[Problem solving process]

A, see the midpoint of the midline, see the midline doubled.

In geometric problems, if the midpoint or midline is given, we can consider using the midpoint as the midline or extending the midline twice to solve related problems.

Secondly, parallel lines are often used in the proof of proportional line segments.

When making parallel lines, one ratio in the conclusion is often kept, and then it is linked with another ratio in the conclusion through an intermediate ratio.

Three, for trapezoidal problems, commonly used methods to add auxiliary lines are

1, the two ends of the upper bottom are perpendicular to the lower bottom.

2. Make a waist-high parallel line at one end of the upper sole.

3. Draw a diagonal parallel line at one end of the upper sole.

4. Make the midpoint of one waist parallel to the other.

5. The straight line passing through the endpoint of the upper sole and the midpoint of the waist intersects with the extension line of the lower sole.

6, which is the trapezoid midline.

7 extend the waist to make it intersect.

Fourthly, in solving the problem of circle.

1, the intersection of two circles is an even chord.

2. Two circles are tangent, and the tangent point leads to the common tangent.

3. Look at the diameter at right angles.

4. In the case of tangent problem, the radius of connecting tangent points is a common auxiliary line.

5. When solving problems related to chords, the chord center distance is often made.