Common methods of geometry proof questions, how to do geometry proof questions

Geometric proof is a hurdle that junior high school students can't bypass. So how do you learn it?

1.Listen carefully to the answers in class and thoroughly understand the basic concepts and theorems in the book.

2.Do more geometry practice questions to find a sense of the problem. Or, whenever you have free time, you can observe and appreciate (not necessarily do) all kinds of geometric proof figures, and build up an intuition about the figure, which is important when proving.

3.The specific method of doing the question in front of Huai:

Read the question carefully and mark the conditions given in the question with a serial number, asking yourself: What do I know from this?

If there are several small problems in a question, you can write them appropriately in sections, so that the teacher can quickly understand your ideas.

Think twice after the proof is over: what else can be done? What other conclusions can be drawn? In order to achieve the effect of doing a question through one piece, it will be one class.

Geometric proofs generally fall into two categories:

1. Prove that the line segments are equal, parallel, perpendicular, and twice as long.

2. Prove that the size of the angle, equal, multiplication.

Common Thinking Methods for Geometry Proof Questions:

1. Simple proof questions, using positive thinking methods.

2. Complex questions should be clearly enumerated, and the reverse thinking method (i.e., the method of thinking about the conditions backwards from the conclusion) and the method of combining forward and backward should be used to prove it.

Solution: There is a functional relationship between the BAC angle and the angle e degree... ACB also has the angle e as x degree and bac as y degree.

y=2x, let acb be x degrees, and bac be y degrees.

y=180-2x

Of course... x,y is scoped...

You know the conditions...

Seeking recognition ...

You can put two 60-degree triangles together, and this happens, but this is only one of them.

You just set the bac to 15 degrees, and any new conclusions that can be deduced from it can be used as a condition for the question.

If you can't find an answer, just two identical unequal right-angled triangles DAC and BAC, with small angles facing outwards and hypotenuse stacked together, you think that there are countless possibilities for such a shape, you can cut it yourself.

The BAC angle is uncertain, so it should be something missing.

In fact, the proof questions in mathematics are not very difficult, the key is confidence and method.

1) It is necessary to master the most basic proof methods and common methods. For example, the proof and writing of triangle congruence, the proof and application of the Pythagorean theorem, the method of using equations and functions in geometric problems, etc.

2) is good at doing auxiliary lines, to master the practice of common auxiliary lines, such as high, vertical lines, etc., of course, the auxiliary line is not the more the better, generally not more than two (must do two auxiliary lines of geometry questions are more difficult questions) in the high school entrance examination geometry problems of the auxiliary line is generally not more than two, in addition to the need to master when to do what kind of auxiliary line, the general situation is for example, for example, to find the area we will make high, in the circle we often even the radius and so on.

3) Of course, you can use algebra (arithmetic and equation functions) to solve some geometric proof problems for some problems.

4) Be good at finding the relationship between known conditions and unknown in the problem, and use flexible and effective methods to solve it, such as the two line segments required to appear in two triangles, then you should study whether the relationship between the two triangles is congruent or similar, and how to prove the congruence or similarity.

5) It is necessary to constantly summarize the practice of various geometric problems, such as the introduction of several auxiliary lines of trapezoids (a total of 7 kinds), how to solve the problems in general circles (often do radius), the proof of tangent lines (even radius, proof vertical), etc., as long as you continue to summarize, I believe you will have something to gain.

Answer: Proof questions in geometry are basically the same as proof questions in mathematics. Mathematical function or equation proof process, left = right; That is, the proof is complete, and the intermediate process is nothing more than the application of formulas and definitions.

The proof of geometry is actually this process, except that the figure, line segment, angle, etc. are taken as an algebraic quantity, and proved by the interrelationship of points, lines, and surfaces; So all that is used are theorems, equiquantitative transformations, and proportional relations. The main relationships are parallel lines, congruent triangles, similar triangles, circumferential angles, central angles, chord tangent angles, and four-point co-circles. Therefore, when you get the proof problem, you have to push from both sides of the equation to the middle, which is equivalent to looking at what the left equation equals?

What is right-style equal? That is to say, if the left and right formulas are equal, we can definitely deduce whether it is a similar triangle problem, a congruent triangle problem, or a parallelogram problem. Is it a problem of circumferential and central angles, or is it a problem of parallel lines. Some problems can not be seen directly, and in the process of analysis, you will know that you are adding auxiliary lines to help you think and solve problems.

In order to master these well, it is necessary to do more questions, and through these trainings, you can improve your personal problem-solving skills and theorems, concepts, and skills. For example, all triangles can be turned into parallelograms; Among them, an isosceles triangle can be transformed into a diamond, a right triangle can be turned into a rectangle, and an isosceles right triangle can be turned into a square; They can all be circumscribed circles and inscribed circles, etc.; When analysis and imagination are not enough to solve problems, sometimes it is possible to use the Pythagorean theorem and trigonometric relations to calculate. All in all, only the skills that can be mastered by doing the questions by yourself are the skills that you can master.

Other people's skills cannot be counted as skills if they are not trained to do problems. It can only be a reference. Because if you don't have the knowledge, you don't have it.

However, the practice of proof questions is inseparable from analyzing from both sides to the middle to find the relationship between equal quantities. This is something that no one can change. As long as it is not perjury, there must be such an equivalence relationship.

Whether you can find it or not is a question of skill in doing problems, and a matter of mastery of theorems, concepts, etc. As long as you do more questions, you will definitely improve your problem-solving ability. Believe in yourself, as long as you work hard, you can succeed!

The road is underfoot.

Certificate: ABO, AO=AB

b= AOB (isosceles triangle).

In the same way, c= cod

ob oc boc = 90° = boa + cod = b + c a = 180 °- b - aob = 180 °-2 b the same way: d = 180 ° - 2 c

a+∠d=180°+180°-2（∠b+∠c）=360°-180°=180°

ab dc (complementary to the paramedial angle),

Absolutely detailed steps, just a little more.

Because ao=ab, b= aob, the same way c= odc, and aob and doc are congruent, then b and c are congruent, because there are two triangles, all the inner angles add up to 360 degrees, c + b + aob odc=180, then the remaining a+ d = 180 degrees, the same side inner angles are complementary, and the two straight lines are parallel ab dc

Connect the BC

Because the angle AOB plus the angle doc 180° 90° 90° and because ab ao, do dc, then the angle abo dco is also equal to 90 ° and because the angle boc is equal to 90°, so the angle obc angle ocb 90°, then the angle abc angle dcb 180°

The isotope angles are complementary, and the two straight lines are parallel.

AB parallel DC

Because the angle BOC = 90° so the angle AOB + angle COD = 90° AO=ab, so the angle B = the angle AOB

do=dc, so angular c=angular doc

So angle b + angle c = 90°

The sum of the inner angles of the triangle is 180°

So angle a + angle d = 180° (360° minus other angles) so parallel.

Angle A = 180 - Angle B - Angle Aob 1 formula.

Angle d = 180-angle c - angle doc 2 formula.

Ao=ab, do=dc

So the angle b = angle aob and the angle c = the angle doc

and ob oc, so the angle AOB + angle doc = 90

So angle b + angle c = 90°

1 + 2.

Angle a + angle d = 360-90-90

So: angle a + angle d = 180

So: ab dc

Just prove that a+d=180 is sufficient.

Obviously, aob+ doc=90

a+∠b+∠aob+∠doc+∠b+∠c=360∠a+∠b=180

So: ab dc

Get 4 pairs of triangles that are similar.

Convert be:de proportionally with the corresponding edges

My mother hates math the most in her life!

Generally, the questions I can't do are wrong, and this question is no exception, the easiest way:

Move point d to near a, then 2ac dc is close to 1 2, and be ed is much greater than this value;

If you don't think this is reliable, you can use special case evaluation comparison.