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, connecting AG intersects with DE at H point, and extending AG intersects with BC at F point ∫ point G is the center of gravity of △ABC, ∴ point F is the midpoint of BC. Football club. ∫d and E are the midpoint of AB and AC, ∴DE is the center line of △ABC, ∴.

1

2

BC,∴HE∥BE,HE=

1

2

BF。 ∴△HEG∽△FBG,∴

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That is eg: BG = 1: 2 in the same way 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.