What is the significance and help of advanced geometry for elementary geometry and high school compe

If it is not recommended that you look at advanced geometry for the competition, including advanced algebra, most or most of the direction of his questions is junior high school knowledge, generally 2 volumes are a plane geometry, a number theory, a combinatorial mathematics, 1 volume is generally slightly more difficult than the college entrance examination It's very simple for the competition, and more practice is a bit useful for the college entrance examination competition Hehe, plane geometry is generally so many theorems (Menelaus's theorem, Seva's theorem, Ptolemy, Simson, Nine Point Garden, etc....). After a long time, some can't remember) There are general competition books Read more, practice more, think more, and generally be very fierce Number theory should be looked at specifically, and the average middle school student can't get in touch, but the exam is not particularly difficult, after all, it's a high school competition, and there are many methods to learn well It may be simpler than the plane Combinatorial mathematics or something I didn't read much at the time Too much I can't see it There is also a must learn the basic courses of high school well, after all, there are still half points in a volume (I didn't pay much attention to it now) A bad test will affect the grades The first volume is to ensure that you win the award The second volume is to ensure that you win the grand prize I hope you get good grades in the exam This year's is almost a few months away Come on.

I'm from the Mathematics Department.

The main role of higher geometry in elementary geometry is, in my opinion, to provide another way of thinking for the proof of collinear points and copoint lines, and it is also the key point. In general, there is not much content in higher geometry, there are few theorems, that is, the description is relatively long, and you must read the conditions clearly when you use them. Most of the middle school math competitions still use the content of elementary geometry, and the theorems in the math textbooks that I usually learn are not enough, but I also have to learn a lot of theorems.

I don't know if you've ever learned elementary geometry for competitions, that one is more useful. For example, the dihedral method in high school mathematics is a difficult point, and it is often impossible to find that angle, but there is a theorem in elementary geometry that can solve many of these difficult dihedral problems.

In the analytic part of the construction system in advanced geometry, I am in high school, and I learned the way to find the plane normal vector of the cross product of a vector, which is a third-order determinant, which is relatively fast. I haven't read the rest yet, and I feel like I'm going to go to university to study hard.

Mathematics competitions themselves are not of general significance, these formulas are summarized for a particular type of problem.

It is known that there are 2*a1+3*b1=-1

2*a2+3*b2=-1

Let the equation of the straight line be ax+by+c=0

then there should be a*a1+b*b1+c=0

a*a2+b*b2+c=0

By the above four formulas.

The answer should be 2x+3y+1=0

Substituting (2,3) into two linear equations yields.

3b1=-1-2a1。。。1

3b2=-1-2a2。。。2

The subtraction of the 1,2 equation yields 3(b1-b2)=-2(a1-a2), so the pq slope k=-2 3

The pq equation is y-b1=-2 3(x-a1), and the shift y=-(2 3)x+(2a1+3b1) 3

From Equation 1, the pq equation is 3y+2x+1=0

Let y=ax+b, then the intercept on the y-axis y0=b, the intercept ax0=-b on the x-axis, then ab=-b*2, then b(a+2)=0

That is, a=-2 or b=0, i.e., y=-2x+b or y=ax point p(2,-1) is substituted into the equation to obtain: -1=-2*2+b, then b=3, i.e., y=-2x+3, i.e., 2x+y-3=0

or -1=a*2, then a=-1 2, i.e., y=-1 2x, i.e., x+2y=0

Let the equation be x a+y b=1 (a is the intercept on the x-axis, b is the intercept on the y-axis) From the problem, we know that 2a=b brings the point p in, so a is equal to b=3, so the equation is x, i.e., 2x+y-3=0

Let the intercept on the x-axis be a, then the intercept on the y-axis is 2a, and the intercept formula has x a + y 2a=1, because p(2,-1) is on a straight line, and its coordinates meet the above equation, so there is 2 a -1 2a=1, and the solution is a=.Then substitute a to get the equation of the straight line.