Proof: Connect AC power.

E is the midpoint of AB and f is the midpoint of BC.

∴EF is the center line of triangle ABC.

∴EF∥AC,EF=AC/2

∫G is the midpoint of CD, and h is the midpoint of AD.

∴GH is the center line of triangular ADC.

∴GH∥AC,GH=AC/2

∴EF∥GH,EF=GH

∴ parallelogram EFGH

2、AC=BD,AC⊥BD

Prove:

EFGH square

∴EF=FG,EF⊥FG

F is the midpoint of BC, and G is the midpoint of CD.

∴FG is the center line of the triangle BCD.

∴FG∥BD,FG=BD/2

∫EF = AC/2，EF∨AC

∴AC=BD,AC⊥BD