I m a junior high school student, and I can t add auxiliary lines to my math geometry

The auxiliary line is actually very skillful, just like some people in the semester factorization of the criss-cross method, with the method, these things need to be accumulated by experience, and at the same time there are certain rules and skills, but if you want to tell you how to do it here, it's really hard to say. This depends on the sensitivity of your usual accumulation of geometric figures, familiarity with the axioms and theorems in books, and even the more typical conclusions you get when you usually do problems, such as the ratio of the intersection of the three middle lines of a triangle to the middle line is 1:2, although this is not a theorem, but you have this conclusion, and then move closer to it, then you have a direction when you draw the line.

You can also get closer to the condition of the question, use the condition, if the question gives the angle bisector, then do you think about the points on the angle bisector to make perpendicular lines on both sides, if the two line segments are given equal, is there an isosceles triangle, use the height, middle line, and top angle bisector on the bottom edge of the isosceles triangle to coincide, and so on. In short, you must have a certain accumulation of graphic properties, the axioms and theorems in the books must be mastered, and the typical conclusions when practicing must also be memorized.

It's imaginative and dependent, but it's also very dependent on your true understanding of the axioms and axioms. For some helpers, you have to go through the theorems that you might use, and then look for the missing helpers.

I think it's better to speculate from the back forward, if such a conclusion needs to be supported by something, then now there are known conditions, if not, use this as an auxiliary line.

Don't look for auxiliary lines too blindly, you can start from the known or from the problem, and slowly deduce

There are bisector lines in the question, which can be perpendicular to both sides.

The line segment bisects the line vertically, and the line can be connected to both ends.

There are two midpoints in the triangle, and when they are connected, they form a median line.

There is a midline in the triangle, and the extension midline is equally long.

proportional, just similar, often to make parallel lines.

If there are all lines outside the circle, cut the center of the circle to connect the lines.

If the two circles are cut inside and outside, make a tangent line through the tangent point.

Two circles intersect at two points and are generally used as common chords.

It is a diameter and forms a semicircle and wants to connect a line at a right angle.

Make equal angles and add a circle to prove that the topic is less difficult.

The auxiliary line is a dotted line, and you should be careful not to change it when drawing.

There are angular bisectors in the diagram, which can be perpendicular to both sides.

You can also fold the graph in half, and the relationship between symmetry and symmetry will appear.

Angles bisector parallel lines, isosceles triangles to add.

Angular bisector line plus perpendicular line, three lines in one to try.

The line segment bisects the line vertically, often connecting the lines to both ends.

It is necessary to prove that the line segment is doubled and halved, and the extension and shortening can be tested.

There are two midpoints in the triangle, and when they are connected, they form a median line.

There is a midline in the triangle, and the extension of the midline is an isomidline.

A parallelogram appears, symmetrically centrically bisecting points.

Make a high line inside the trapezoid, and try to pan it around the waist.

It is common to move diagonal lines in parallel and make up triangles.

The certificate is similar, than the line segment, and it is customary to add parallel lines.

For equal area sub-proportional exchange, it is very important to find line segments.

It is directly proved that there is difficulty, and the same amount of substitution is less troublesome.

A high line is made above the hypotenuse, and a large piece of the middle item is proportional.

The radius is calculated with the chord length, and the chord centroid distance comes to the intermediate station.

If there are all lines on the circle, the tangent points are connected with the radius of the center of the circle.

The Pythagorean theorem is the most convenient for the calculation of the tangent length.

To prove that it is a tangent, the radius perpendicular line is carefully identified.

It is a diameter and forms a semicircle and wants to form a right-angle diameter chord.

The arc has a midpoint and a central circle, and the vertical diameter theorem should be memorized.

The two chords on the periphery of the corner, the diameter and the end of the chord are connected.

The string is cut to the edge of the tangent string, and the same arc is diagonally to the end.

To make a circumscribed circle, make a perpendicular line on each side.

It is also necessary to make an inscribed circle, and the bisector of the inner angle dreams come true.

If you encounter intersecting circles, don't forget to make common chords.

Two circles tangent inside and outside, passing through the tangent point of the tangent line.

If you add a connecting line, the tangent point must be on it.

It is necessary to add a circle at equal angles to prove that the topic is less difficult.

The auxiliary line is a dotted line, and you should be careful not to change it when drawing.

Basic drawing is very important, and you must be proficient in mastering it at all times.

It is necessary to be more attentive to solving problems, and often summarize the methods.

Don't blindly add lines, and the method should be flexible and changeable.

Analyze and choose comprehensive methods, no matter how many difficulties there are, they will be reduced.

Generally, it can be used as the middle line method, the perpendicular line method, the middle perpendicular line method, and the third equinox point connection method. Geometry is mainly about doing more, and doing more will give you a feeling.

It's not too late for the second model, so hurry up and find this kind of topic to do.

It is recommended to find a booklet "How to Add Auxiliary Lines" for middle school students extracurricular reading book "How to Add Auxiliary Lines" by Shanghai Education Publishing House, the content is very good, and I have forgotten it for a long time. Books can be found online in pdf format.

Connect known points, or make parallel lines.