I. Detailed explanation
1.？ Heart: The intersection of bisectors of three angles is also the center of the inscribed circle of a triangle.
2.？ Eccentricity: the intersection of three perpendicular lines is also the center of the circumscribed circle of the triangle.
3.？ Center of gravity: the intersection of three midlines.
4.？ Vertical center: the intersection of straight lines of three heights.
5.？ Paracenter: the intersection of an internal angle bisector and the external angle bisectors of the other two internal angles.
Second, the concept of triangle
Triangle is a closed figure composed of three line segments on the same plane but not on the same straight line, which has applications in mathematics and architecture.
Ordinary triangles are divided into ordinary triangles (three sides are unequal) and isosceles triangles (isosceles triangles with unequal waist and bottom and isosceles triangles with equal waist and bottom, that is, equilateral triangles); According to the angle, there are right triangle, acute triangle and obtuse triangle, among which acute triangle and obtuse triangle are collectively called oblique triangle.
A closed figure composed of three line segments that are not on the same straight line is called a triangle. A figure surrounded by three straight lines on a plane or three arcs on a sphere is called a plane triangle; A figure surrounded by three arcs is called a spherical triangle, also known as a triangle.
A closed geometry consisting of three line segments connected end to end is called a triangle. Triangle is the basic figure of geometric figure.
The nature of the outer center of triangle
I. Property 1
The outer center of the acute triangle is in the triangle; The outer center of the right triangle is on the hypotenuse and coincides with the midpoint of the hypotenuse; The outer center of an obtuse triangle is outside the triangle.
Two. Nature 2
The perpendicular lines of the three sides of a triangle intersect at a point, which is the center of the circumscribed circle of the triangle, and the distances from the outer center to the three vertices are equal.
Three. Nature 3
If point G is a point on the plane ABC, then the necessary and sufficient conditions for point G to be the center of ⊿ABC are: (vector GA+ vector GB), vector AB= (vector GB+ vector GC), vector BC= (vector GC+ vector GA), and vector CA= vector 0.