如图,△ABC与△DCB中,AC与BD交于点E,且∠A=∠D,AB=DC.(1)求证:△ABE≌△DCE;(2)当∠AEB=52°

2025-05-13 12:48:30
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回答(1):

(1)证明:在△ABE和△DCE中,

∠AEB=∠DEC
∠A=∠D
AB=CD

∴△ABE≌△DCE(AAS);

(2)解:∵△ABE≌△DCE,
∴BE=CE,
∴∠EBC=∠ECB,
又∵∠AEB=∠EBC+∠ECB=52°,
∴∠EBC=26°.