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.

Second,

In the proof of proportional line segments, parallel lines are often made.

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、

Both ends of the upper bottom surface are perpendicular to the lower bottom surface.

2、

A waist-high parallel line passes through one end of the upper sole.

3、

A parallel line passing through one end of the upper sole forms a diagonal line.

4、

The midpoint of one waist is parallel to the other.

5、

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

6、

Trapezoidal midline

seven

Extend the waist so that it intersects.

Fourthly, in solving the problem of circle.

1, the intersection of two circles is a chord.

2

Two circles are tangent, and the tangent points lead 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.

These are the common auxiliary lines that I summarized.