∴AB=CD AD=BC(平行四邊形的對(duì)邊相等)
AO=CO BO=DO(平行四邊形對(duì)角線互相平分)
AB=BC CD=AD(菱形的定義)
∴AB=BC=CD=AD(等量代換)
即:菱形的四條邊都相等
∴△ABO≌△CBO △BCO≌△DCO △ADO≌△CDO △ABO≌△ADO (SSS)
∴∠ABO=∠CBO ∠BCO=∠DCO ∠CDO=∠ADO ∠BAO=∠DAO
∠AOB=∠COB ∠BOC =∠COD ∠COD=∠AOD ∠AOD=∠AOB(全等三角形的對(duì)應(yīng)角相等)
∵∠AOB+∠BOC+∠COD+∠AOD=360°
∴∠AOB=∠BOC=∠COD=∠AOD=90°
∴菱形的四條邊都相等;菱形的兩條對(duì)角線互相垂直,并且每一條對(duì)角線一組對(duì)角.
