Cut out a parallelogram with cardboard so that the intersection of its diagonals is O, fix a straight thin wooden strip lying flat on the parallelogram at 0 o'clock with a pin, and stir the thin wooden strip to make it stay at any position at will. What did you find by observing the results of several strokes? Prove your findings.
Answer: If the edge and mouth ABCD of the batten intersect at point E and point F respectively, we can find OE=OF, AE=CF, DE = BF, △ AOE △ COF.
△ DCE △ BOF, etc.