證明：?$(1)$?∵?$AB=CD$?
∴?$\widehat {AB}=\widehat {AC}$?，
即?$\widehat {BC}+\widehat {AC}=\widehat {AD}+\widehat {AC}$?
∴?$\widehat {AD}=\widehat {BC}$?
解：?$(2)$?連接?$AC$?
∵?$\widehat {AD}=\widehat {BC}$?
∴?$AD=BC$?
又∵?$CD=AB$?，?$AC=AC$?
∴?$△ADC≌△CBA(\mathrm {SSS})$?
∴?$∠ACD=∠CAB$?
∴?$AE=CE$?
