The auxiliary lines of proving problems of mathematics and geometry in junior middle schools are generally drawn as dotted lines. According to the principle of revealing the hidden nature of graphics and gathering letters together in trembling, three basic points of the function of graphics are constructed.
1. Reveal the properties implied in the graph: When the logical relationship between the condition and the conclusion is unclear, fully reveal the properties of the graph implied in the condition by adding appropriate auxiliary lines. So as to draw a transitional inference and reach a conclusion. ?
2. Concentration principle: By adding appropriate auxiliary lines, the scattered and distant elements in the graph are relatively concentrated and gathered on the related graph through transformation, thus establishing the logical relationship between the topic setting conditions and the conclusion, and deducing the required conclusion.
3. The function of constructing graphics: For a geometric proof, some graphics are often needed, which cannot be found in the graphics given in the topic setting conditions. Only by adding up these pictures can we draw a conclusion. Common methods include constructing sum-difference multiples of line segments and angles, new triangles, right triangles, isosceles triangles and so on.
Drawing method of triangle auxiliary line;
Methods 1: The midline of triangle is always 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.
Method 2: When there is a bisector, we often take the angular bisector as the symmetry axis, use the properties of the angular bisector and the conditions in the problem to construct a congruent triangles, and use congruent triangles's knowledge to solve the problem.
Method 3: The conclusion is that when two line segments are equal, auxiliary Templeton lines are often drawn to form congruent triangles, or some theorems about bisecting line segments are used.
Method 4: The conclusion is that the sum of one line segment and another line segment is equal to the third line segment, and truncation method or complement method is often used. 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.