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

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.

The key is to do more questions, summarize more, and decide whether to do auxiliary lines and how to do them according to specific questions.