The center of gravity is the intersection of three sides of a triangle, and the intersection of three lines can be proved by the dovetail theorem, which is very simple. The proof process is a special case of Seva theorem.

Several properties of the center of gravity:

1, and the ratio of the distance from the center of gravity to the vertex to the distance from the center of gravity to the midpoint of the opposite side is 2: 1.

2. The areas of the three triangles formed by the center of gravity and the three vertices of the triangle are equal.

3. The sum of squares of the distances from the center of gravity to the three vertices of the triangle is the smallest.

4. In the plane rectangular coordinate system, the coordinate of the center of gravity is the arithmetic average of the vertex coordinates, that is, its coordinate is ((x 1+x2+x3)/3, (y1+y2+y3)/3); Spatial Cartesian Coordinate System-abscissa: (X 1+X2+X3)/3

Ordinate: (Y 1+Y2+Y3)/3

Ordinate: (z 1+z2+z3)/3

5. The point where the product of the distance from a triangle to three sides is the largest.

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The three midlines must intersect, and the intersection position is really strange.

The intersection is named "center of gravity", and the nature of the center of gravity should be clear.

In the center of gravity segmentation, you can hear the ratio of line segment to several segments;

The ratio of length to length is two to one, so we should use it flexibly and master it well.