Put your finger against a point in the plane figure. If the plane figure can keep balance, then this point is called the center of gravity of the plane figure. The center of parallelogram is the intersection of diagonal lines, and the center of gravity of triangle is the intersection of three midlines. Please use the following figure to prove that the ratio of two line segments formed by dividing the center of gravity of a triangle into a middle line is 1: 2, that is, in △ABC, BE and CD are two middle lines, and they intersect at G, so verify:

Solution: As shown in the figure, connect AG, cross DE at H point, and extend AG across BC at F point.

G point is the center of gravity of △ABC,

Point f is the midpoint of BC.

∴BF=FC.

D and e are the midpoint of AB and AC,

∴DE is the center line of △ABC,

∴DE∥BC,DE=

1

2

BC,

∴HE∥BE,HE=

1

2

BF。

∴△HEG∽△FBG，

∴

ge

gbyte

=

male

novio

=

1

2

That is eg: BG = 1: 2.

Similarly DG: CG = 1: 2.

∴DG:CG=EG:BG= 1:2.

2. take the midpoint m and n of BG and CG and connect them. It is proved that all triangles DEG are equal to triangle MGN, and then DG=NG and EG=MG, so DG= 1/2CG and EG= 1/2BG, so DE: BC = DG: CG = EG: BG = 1: 2.