Again? ABD=？ CDB？ AB//DC。

? The quadrilateral ABCD is a parallelogram (two groups of parallelograms with opposite sides are parallelograms).

Proof 2: ∵? ADB=？ CBD，

? ABD=？ CDB，DB=BD，

? △ Abd△ ?△CDB(ASA).

? AD = BC, AB=DC.

? Quadrilateral ABCD is a parallelogram (two groups of quadrangles with equal opposite sides are parallelograms).

Prove 3: From Prove 1, we know AD∑BC, and from Prove 2, we know AD=BC.

? The quadrilateral ABCD is a parallelogram.

A set of quadrilaterals with parallel and equal opposite sides is a parallelogram.

2. Prove that 1: ∵ quadrilateral ABCD is a parallelogram,

? AD∨BC，AD=BC。

Point e and point f are the midpoint of AD and BC, respectively.

? DE= 1/2AD，BF= 1/2BC，？ DE-=BF。

? Quadrilateral BEDF is a parallelogram (a group of parallelograms with equal opposite sides are parallelograms).

Prove that 2: ∵ quadrilateral ABCD is a parallelogram,

? AB=DC，？ A=？ c，AD=BC。

Point e and point f are the midpoint of AD and BC, respectively.

? AE= 1/2AD，CF= 1/2BC，？ AE=CF。

? △ABE?△CDF(SAS)。

? BE=DF。

AD = BC，AE=CF，？ DE=BF。

? Quadrilateral BEDF is a parallelogram.

Two sets of quadrilaterals with equal opposite sides are parallelograms.

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