?$證明：?(1)?∵四邊形?ABCD?是平行四邊形，$?
?$∴?AB//CD，?$?
?$∴?∠GAE=∠HCF，?$?
?$∵點(diǎn)?G，??H?分別是?AB，??CD?的中點(diǎn)，$?
?$∴?AG=CH，?$?
?$∵?AE=CF，?$?
?$∴?△AGE≌△CHF(\mathrm {SAS})，?$?
?$∴?GE=HF，??∠AEG=∠CFH，?$?
?$∴?∠GEF=∠HFE，?$?
?$∴?GE//HF，?$?
?$又∵?GE=HF，?$?
?$∴四邊形?EGFH?是平行四邊形．$?
?$?(2)?連接?BD?交?AC?于點(diǎn)?O，?$?
?$∵四邊形?ABCD?是平行四邊形，$?
?$∴?OA=OC，??OB=OD，?$?
?$∵?BD=14，?$?
?$∴?OB=OD=7，?$?
?$∵?AE=CF，??OA=OC，?$?
?$∴?OE=OF，?$?
?$∵?AE+CF=EF，?$?
?$∴?2AE=EF=2OE，?$?
?$∴?AE=OE，?$?
?$又∵點(diǎn)?G?是?AB?的中點(diǎn)，$?
?$∴?EG?是?△ABO?的中位線，$?
?$∴?EG=\frac {1}{2}OB=3.5．?$?
?$∴?EG ?的長為?3.5?$?
