证明：∵$∠AEC$是$\triangle ABE$的外角，∴$∠AEC = ∠B+∠BAE$
∵$∠AEC=∠AED+∠CED，$$∠B = ∠AED，$∴$∠BAE=∠CED$
$ $在$\triangle ABE$和$\triangle ECD$中
$\begin {cases}∠BAE=∠CED\\∠B=∠C\\BE = CD\end {cases}$
∴$\triangle ABE≌\triangle ECD(\mathrm {AAS})$
∴$AE = ED，$∴$∠EAD=∠EDA$
