If you take part in the high school mathematics competition, there must be a plane geometry in the three major questions in the second interview, and these theorems are generally used, especially Menelaus and Seva, a proof point * * * line and a proof line * * * point.

However, if you don't want to take part in the math contest, don't spend time on it. I won't take the college entrance examination. Too much research will delay your normal study. If you don't take part in the math contest and are only interested, don't spend too much time on it.

Speaking of the significance of mathematics, it is for a subject. The development of a discipline will have many branches. Some will help people to continue their research as tools, and some may not show advantages at that time, but they will inspire people who study this subject. Let me give you an example. These theorems explain * * * points from the perspective of plane geometry. * * * line, etc. In practice, we often use analytic geometry to * * * points and * * * lines, but the answer of analytic geometry is right (assuming we don't know whether analytic geometry is right or not), but we can interpret it from another angle through these theorems, which is very useful for the rigor of mathematics. If the answer of analytic geometry is different from that of plane geometry (assuming there are different answers), it shows that our existing part of mathematics is not rigorous, and the imprecise foundation will lead to great problems in later calculation and application, so it is very necessary to learn mathematics from all aspects.