2) The triangle is divided into six small pieces by three median lines, and the areas of the six small pieces are equal, that is to say, the connecting line between the center of gravity and the three vertices divides the area of the triangle into three equal parts. 【 Prove: The areas of triangles with equal bases and equal heights are equal. The area of a triangle with twice the height and twice the bottom is equal to the area of a triangle with twice the height and twice the bottom]
2) For a triangular object with uniform material, its center of gravity is on the geometric center of gravity. In other words, you can cross a line from the center of gravity and hold the line with your hand, while the triangular object remains horizontal.
The five centers of a triangle
A theorem
Gravity center theorem: Three midlines of a triangle intersect at a point, which is the vertex.
The distance is twice the distance from the opposite midpoint. This point is called the center of gravity of the triangle.
Eccentricity theorem: the perpendicular lines of three sides of a triangle intersect at one point. This point is called the outer center of the triangle.
Vertical center theorem: three heights of a triangle intersect at one point. This point is called the center of the triangle.
Interior Theorem: The bisectors of three interior angles of a triangle intersect at one point. This point is called the heart of a triangle.
Proximity theorem: the bisector of the inner angle of a triangle intersects the bisector of the outer angle of the other two vertices at one point. This point is called the center of the triangle. A triangle has three side centers.
The center of gravity, outer center, vertical center, inner center and lateral center of a triangle are called the five centers of the triangle.