OE⊥AB? OF⊥BC OM⊥CD ON⊥DA
Because it is a parallelogram.
So OE and OM are on the same line.
In the same way, OF and ON are on the same line.
The area formula is: bottom * height /2.
S△AOB+S△COD = AB * OE/2+CD * OM/2 = AB *(OE+OM)/2(AB = CD)
S△AOD+S△COB = BC * OF/2+AD * ON/2 = BC *(OF+ON)/2(BC = OD)
Because OE+OM is the height of the parallelogram when AB or CD is the base.
When BC or DA is the base, OF+ON is the height of parallelogram.
So S△AOB+S△COD=AB*(OE+OM)/2=S parallelogram /2.
? S△AOD+S△COB=BC*(OF+ON)/2=S parallelogram /2
So S△AOB+S△COD=S△AOD+S△COB.
2. According to the fact that the parallelogram is a central symmetric figure and the center of symmetry is the center of the parallelogram, the line where the diagonal of the well intersects with the parallelogram bisects the ground.
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