1, center of gravity: the center of gravity of a triangle is the intersection of three midlines, and the length of its connecting line with each vertex is equal to twice the distance from the vertex to the midline. This property is very important in geometry and can be used to prove and calculate. For example, the center of gravity of an equilateral triangle divides the triangle into three equal parts, each of which contains a vertex and a midline.
2. Vertical center: The vertical center of a triangle is the intersection of three high lines. An interesting property is that the vertical center of any triangle can only be adjacent to one vertex of the triangle. This property can be used to prove some geometric problems.
3. Exterior center: The exterior center of a triangle is the intersection of the vertical lines of the three sides, also called the center of the circumscribed circle of the triangle. The distance from the outer center of a triangle to the three vertices is equal, which is often used to prove and calculate in geometry. For example, the outer center of an equilateral triangle is also its center of gravity and vertical center.
4. Inner heart: The inner heart of a triangle is the intersection of the bisectors of three inner angles. The distance from the heart to the three sides of a triangle is equal, which is called the nature of the heart in geometry. This property can be used to calculate and prove some geometric problems. For example, the inner heart of an equilateral triangle is also its outer center, center of gravity and center of gravity.
The application of triangle in mathematics;
1. Application of Pythagorean Theorem: Pythagorean Theorem is an important property of triangles, pointing out that in a right triangle, the square of hypotenuse is equal to the sum of squares of two right-angled sides. This theorem can be used to solve various problems, such as measuring distances that cannot be measured directly and calculating angles that cannot be measured directly. Pythagorean theorem can also be used in computer science, physics, engineering and other fields.
2. Application of equilateral triangle and isosceles triangle: equilateral triangle and isosceles triangle are two special types of triangles, each with its own unique properties and uses. An equilateral triangle has three equilateral sides and three internal angles, which can be used to solve some geometric problems, such as calculating angles and proving theorems. An isosceles triangle has two isosceles and two equal base angles, which can be used to make some symmetrical figures and solve some symmetrical problems.
3. Application of trigonometric functions: trigonometric functions are some important functions in triangles, which can be used to describe the properties of triangles and solve some geometric problems. For example, sine function can be used to calculate angle, cosine function can be used to calculate length, tangent function can be used to calculate slope and so on. Trigonometric functions can also be used in computer science, physics, engineering and other fields.