解：?$(1)$?∵?$EB = AB，$?∴?$∠E = ∠EAB$?
∵?$DB = AB，$?∴?$∠D = ∠DAB$?
∵?$∠EAB + ∠DAB + ∠E + ∠D = 180°$?
∴?$2∠EAB + 2∠DAB = 180°，$?即?$∠EAB + ∠DAB = 90°$?
∴?$∠DAE = 90°，$?∴?$?ADE$?是直角三角形
?$(2)$?∵?$AB = AC，$?∴?$∠ABC = ∠ACB$?
∵?$BE = BC，$?∴?$∠BEC = ∠BCE$?
∴?$∠ABC = ∠BEC$?
∵?$DB = DE，$?∴?$∠DBE = ∠DEB$?
∴?$∠ADE=2∠DBE$?
∵?$DE=AE，$?∴?$∠A=∠ADE$?
∴?$∠A=2∠DBE$?
∵?$∠BEC=∠DBE+∠A，$?∴?$∠BEC=3∠DBE$?
∵?$∠A+∠ABC+∠ACB=180°$?
∴?$2∠DBE+3∠DBE+3∠DBE=180°$?
∴?$∠DBE=22.5°$?
∴?$∠A=2∠DBE=45°$?
∵?$DE=AE，$?∴?$∠ADE=∠A=45°，$??$∠AED=90°$?
∴?$△ADE$?是等腰直角三角形
