设AC、BD相交于O
∵菱形ABCD,∴OA＝OC,OB＝OD,AC⊥BD
又AE＝CG,BF＝DH,∴OE＝OG,OF＝OH
∴△EOF≌△GOH≌△EOH≌△GOF,∴EF＝FG＝GH＝HE
∴四边形EFGH是菱形