The midpoint quadrilateral is a relatively new knowledge in recent years. First of all, we must know that all midpoint quadrangles must be parallelograms. You can make any quadrilateral and then connect any two diagonals. According to the nature of the midline in a triangle, it can be proved that the opposite sides of 1 group are parallel and equal, thus proving that this quadrilateral acts as a parallelogram. From this proof, we can draw the inference that the midpoint quadrangle is related to the diagonal of the initial quadrangle. The concrete conclusions are as follows: If the diagonals of the original quadrangle are equal, the four sides are parallel and equal. If the diagonal of the original quadrangle is vertical, the midpoint quadrangle is rectangular. This is easy to prove. The landlord should draw a picture by himself and experience it. After all, mathematics is to be understood. The nature of parallelogram: two groups of opposite sides are parallel and equal, diagonal lines are equally divided and diagonal lines are equal. Definition: Two groups of parallelograms with opposite sides are parallelograms. All of the above can be obtained by connecting diagonal lines and proving triangle congruence. As for the diamond, it not only has all the properties of a parallelogram, but also: the diagonals are perpendicular to each other, a set of diagonals bisects a set of diagonals, and all four sides are equal. We call a group of parallelograms with equal adjacent sides a rhombus (definition), and a rectangle also has all the properties of a parallelogram. In addition, the diagonals are equal. It is also a property that all four angles are right angles. We call a parallelogram with an internal angle of 90 a rectangle. A square has the properties of the above three special quadrangles. We call a group of rectangles with equal adjacent sides a square. I don't think there is anything to say about the special triangle. If it is not the third grade, you will be very clear about the relationship between three sides and angles when you learn trigonometric functions. These are easy to prove. I'll add one for you. There should be no such thing in the current textbooks: the intersection of the three midlines of a triangle is called the center of gravity, which divides each midline into two parts: 1:2 (that is, the center of gravity is the bisector of each midline). If so, I'll give you some tips. First of all, these geometric theorems should be subconscious and you can't memorize them. Of course, you can't forget them If you haven't entered the third grade, you'd better preview it first. Especially in the third grade, such as some difficulties and hot spots in the senior high school entrance examination: quadratic function and circle. Personally, I think you should finish them by yourself when you graduate from the second grade. In the third grade, you should follow the teacher to do more questions and certification. Will not feel strange (have a deep understanding). Judging from the trend in 2008 and 2009, quadratic function is still the last question. As for the circle, it usually involves about one in the fill-in-the-blank question and about one in the geometric proof question. I have read this year's examination paper. Personally, I think Chengdu is the most difficult problem to prove. Watching more can improve your imagination of geometric space, and you won't feel hard to learn solid geometry or even trajectory equation in high school.

It is very important to add auxiliary lines in the proof questions. 1. For fixed pattern graphics such as "x, a", it is most important to add the center line or parallel line, but it should be added according to the question type and do more exercises. 2. General geometric proofs are all within a quadrilateral, so it is very important to understand the properties of quadrilateral. It is very important to supplement the auxiliary line, or analyze it according to the question type. Don't worry (I suffered a loss because of this in the third grade). 3. After you learn the circle, you will do some proofs about the circle, generally combining triangles and quadrangles, but not much. The best auxiliary lines in a circle are connecting radii, making vertical chords, etc. These are all related to the theorem in the circle. I remember there were so many exams in junior high school geometry. If you don't understand, you can ask them. I'll explain it for you when I have time. The second module should be a function. Most students will get two kinds of functions in the senior high school entrance examination or school examination (grade three), namely quadratic function and inverse proportional function. Of course, if the questioner is smart, he will definitely combine them with linear functions and geometric figures, which are generally used as the finale questions. You probably haven't learned it yet, so I'll sum up the processing method of the quadratic function synthesis problem in the senior high school entrance examination. 1 there are some problems, that is to say, let. Straight line, etc. , form the quantitative relationship, positional relationship and special graphics that meet the meaning of the question. Among them, the existence of isosceles triangle and RT triangle is subdivided. The method to solve the existence of isosceles triangle points is generally to use the point distance (the distance formula between two points, that is, let any two points coordinate a (x 1, y 1) and b (x2, y2), then -(y 1-y2)? Note that the root sign is above the whole formula). For Rt△, it is generally used as an auxiliary line (80% perpendicular to the known straight line) to prove the similarity of triangles. For the two major problems of quadratic function, my method is based on your equation that is not quartic, so just pay attention to this. 2. The problem of maximum and fixed value. Generally, the maximum value of a geometric figure will be found, so that this geometry can be found. It is more difficult to find the maximum value by using vertex coordinates or formulas. Subdivided into: transform the fixed value and find the fixed value by geometric relationship. The most important thing is to find the relationship between the quantity required in the topic and the quantity to be composed, which is the basis of establishing the equation. After all, functional thinking is closely combined with equations. Other functions, but also more difficult knowledge, do not want to play here (sorry, my hand hurts). You can also ask me another day.