1

Method of adde auxiliary lines in triangle problem

The median line of a (1) triangle is often double. Questions with a midpoint, usually the center line of a triangle. By this method, the conclusion to be proved is properly transferred, and the problem is easily solved.

(2) For problems with bisectors, we often take the angular bisector as the axis of symmetry, and use the properties of the angular bisector and the conditions in the problem to construct congruent triangles, so as to use congruent triangles's knowledge to solve the problem.

(3) The conclusion is that when two line segments are equal, auxiliary lines are often drawn to form congruent triangles, or some theorems about bisecting line segments are used.

(4) The conclusion is that the sum of one line segment and another line segment is equal to the third line segment, which is usually truncated or supplemented. The so-called truncation method is to divide the third line segment into two parts and prove that one part is equal to the first line segment and the other part is equal to the second line segment.

2

Addition of common auxiliary lines in parallelogram

The two groups of opposite sides, diagonal lines and diagonal lines of parallelogram (including rectangle, square and diamond) all have some similar properties, so there are some similarities in the method of adding auxiliary lines. The purpose is to create parallelism and verticality of line segments, form congruence and similarity of triangles, and transform parallelogram problems into common problems such as triangles and squares. Common methods are as follows, for example:

(1) connect diagonal or translate diagonal;

(2) constructing a right triangle with the vertex as the edge and the vertical line;

(3) connecting a diagonal intersection with the midpoint of one side, or a parallel line intersecting the diagonal intersection as one side, to form a line segment parallel line or midline;

(4) connecting a line segment with vertices and points on opposite sides or extending the line segment to form a triangle with similar or equal products;

(5) The vertical line intersecting the vertex diagonally constitutes a parallel line segment or triangle congruence.

three

Method of adding common auxiliary lines in a circle

In plane geometry, when solving problems related to circles, it is often necessary to add appropriate auxiliary lines to connect the problems and conclusions, so that the problems can be solved naturally. Therefore, mastering the general rules and methods of auxiliary lines flexibly is of great help to improve students' ability to analyze and solve problems.

(1) considers the chord as the distance from the center of the chord. For the chord problem, the chord center distance (sometimes the corresponding radius) is often made, and the connection between the topic and the conclusion is communicated through the vertical diameter bisection theorem.

(2) Take the diameter as the angle of circumference. If the diameter of a circle is known in the topic, it is generally the circumferential angle opposite to the diameter, and the problem is proved by using the characteristic that the circumferential angle opposite to the diameter is a right angle.

(3) See tangent as radius. The condition of the proposition includes the tangent of the circle, which is often the radius connecting the tangent points. This paper proves this problem by using the property that the tangent is perpendicular to the radius.

(4) The tangents of two circles are common tangents. For the problem of tangency between two circles, the common tangent of two circles or their connecting lines is generally made by the tangent point, and the relationship between the angles related to the circles can be obtained by the common tangent.