Known: as shown in the figure, the quadrilateral ABCD is a parallelogram, e and F are two points on the straight line BD, and de = BF. (1) prove: AE = CF; (2) connect AF and CE, then is the quadrilateral afce a parallelogram?

It is proved that: (1) the ∵ quadrilateral ABCD is a parallelogram, ∥ ad ∥ BC, ad = BC. ∥ ADB = ∥ CBD. ∥ ade = ∥ CBF. De = BF, ∥ ade ≌ CBF. ∥ AE = cf. (2) the quadrilateral afce is a parallelogram

It is known that E and F are on the straight line of the diagonal BD of the parallelogram ABCD, and de = BF

Certification:
Parallelogram ABCD
AB=CD
BF=DE
AB-BF=CD-DE
AF=CE
AF‖CE
So the quadrilateral afce is a parallelogram

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