Wow, this Peking University student is really amazing!In order to let his daughter, who is in junior high school, learn mathematics well, he has put a lot of effort into it.
The handwritten geometric model data is simply too professional!I dare say that this information is more intimate and practical than any auxiliary line formulas, models and conclusions, and model dynamics.
First, let's talk about the auxiliary line mantra skills. As we all know, in mathematical geometry problems, auxiliary lines are the key to the key. Sometimes, a right guide line can make the difference.
This schooly father also sorted out some auxiliary line mantra skills, such as "the sum of the inner angles of the triangle is 180 degrees, and the wrong angles in the parallel lines are equal" and so on. The mantras are simple and easy to understand, and they are practical enough for children to grasp easily.
Let's talk about the model and the conclusions. In mathematical geometry problems, there are many common models and conclusions, such as "the middle line on the bottom edge of an isosceles triangle is equal to half of the base edge", "the middle line of the hypotenuse of a right triangle is equal to half of the hypotenuse", and so on.
These conclusions are proven and can be used directly, providing a lot of convenience for children to solve math problems.
Finally, let's talk about the model dynamics. Sometimes, a static graphic makes it difficult for children to understand the essence of the problem. The model dynamic diagram can let children see the change process of the graph in an intuitive way, so as to better understand the meaning of the question.
For example, when explaining the "inscribed quadrilateral of a circle", the dynamic diagram of the model can clearly show that the distance from the center of the circle to the quadrilateral is equal, so that they can better understand the properties of the inscribed quadrilateral of the circle.
Let's take an example. For example, in the triangle ABC, ab=ac, and AD is the height of the edge of bc. Verify: bd=cd.
At this point, we can use the conclusion that the middle line on the bottom edge of the isosceles triangle is equal to half of the bottom edge. Because ab=ac, d is the midpoint of bc, so bd=cd. This makes it easy to prove the conclusion.
Let's take another example. For example, in a rectangular ABCD, AE is perpendicular to BD to E, and EC is perpendicular to AD to F. Verification: The quadrilateral AECF is a square. At this time, we can understand the problem through the model dynamics.
First of all, due to the nature of the rectangle, we know that AD is parallel to BC, so AECF is a parallelogram. Then, since AE is perpendicular to BD to E and EC is perpendicular to AD to F, AE=EC can be derived. This proves that the quadrilateral AECF is a square.
One last example. For example, in the circle O, ab is the diameter, Cd is a string, and Ab is perpendicular to Cd. Verification: CB=DA. At this time, we can understand the problem through the model dynamics.
First of all, we can take an arbitrary point E on the circle O, connect AE and extend the intersection of Cb at the point F. Since AB is the diameter, AE is perpendicular to CB. And because AB is perpendicular to CD, we can conclude that the quadrilateral CFF is rectangular. This proves that CB=DA.
If you have children, please collect it!Let children seize the time to learn, practice, memorize and skillfully master and flexibly use these knowledge points, and easily get high scores in mathematics!If you have a piece of furniture at home, it is recommended to start with a copy of "Junior High School Mathematics." Geometric Auxiliaries" systematic Xi.
Middle School Mathematics Geometry Auxiliary Line is a learning Xi tutorial book for junior high school mathematics geometry problems. It covers a variety of common geometry guide line methods and techniques and is designed to help students solve a variety of geometry problems.
The main contents of the book include:
Angular bisector auxiliary line: The construction of congruent triangles by using angular bisector is one of the important methods to solve geometric problems. This book explains in detail how to use bisector auxiliary lines in problems, such as by extending the extension of the BE and CD lines at a point.
Truncation and complement the short construction congruence: It is a common method to solve geometric problems by intercepting long line segments or complementing ** segments to construct congruent triangles. This book explains in detail how to use truncation in the problem, such as intercepting ae=ac on ab, and then proving the conclusion by the trilateral relationship of congruence and forming a triangle.
Three-in-one construction of isosceles triangle: Using the properties of three-in-one to construct an isosceles triangle is one of the important methods to solve geometric problems. This book explains in detail how to use the three-in-one method in the problem, such as extending this perpendicular line to intersect the other side to obtain an isosceles triangle, and then perform a congruence proof.
Angular bisector + parallelism: It is a common method to solve geometric problems by using the properties of angular bisector and parallel lines to construct congruent triangles or parallelograms. In this book, we explain in detail how to use the angle bisector + parallel line method in the problem, such as passing the C point as the AD perpendicular line, and the congruence can be obtained.
In addition, this book provides a large number of example problems and practice Xi for different types of problems, so that students can master various geometric auxiliary line methods and techniques through practice.
Overall, "Middle School Mathematics and Geometry Auxiliary Lines" is a very practical Xi tutorial book, which is suitable for junior high school students to read and learn Xi. By reading this book, I believe you will be able to better grasp the knowledge of geometry and improve your ability to solve geometric problems.