The main basis for equal sharing is:

"The straight line passing through the center of symmetry of any closed central symmetric figure must divide the area of this figure equally."

The condition of "closed figure" here is to ensure that this centrally symmetric figure has a fixed area.

Generally speaking, the straight line passing through the symmetry center of any central symmetric figure must divide the original figure into two congruent figures.

For example, according to your knowledge of the second day of junior high school, it is not difficult to prove that any straight line passing through the symmetrical center of a parallelogram will divide it into two congruent triangles or quadrilaterals.

There are two rectangles in the graph you give. A straight line passing through the center of a large rectangle divides the large rectangle into two parts with equal area (marked as S 1 = S2), and a straight line passing through the center of a small rectangle also divides the small rectangle into two parts with equal area (marked as S3 = S4), so S 1-S3 = S2-S4. This shows that this straight line divides the area of the original figure into two parts.

The diagonal line in the figure is to find the center of symmetry. If the diagonal is removed and only two symmetrical centers are left, it is very easy to understand the figure. )

In addition to this method, there are two other similar methods to divide the area of the original graph equally.

(reference:/jswyc/blog/item/5f10c751fa32c1551038c2de.html).

Jiangsu Wu Yunchao answered for reference!