Question

3．（2012•嘉兴）如图,△ABC与△DCB中,AC与BD交于点E,且∠A=∠D,AB=DC．

Answer 1

∵∠A+∠ABE=∠CEB ∠D+∠DCE=∠CEB

∴∠CEB=∠DCE

∵∠A=∠D,AB=DC ∠CEB=∠DCE

∴△ABE ≌ △DCE

∵△ABE ≌ △DCE

∴AE+EC=DE+EB

∴AC=DB

∵AC=DB ∠A=∠D,AB=DC

∴△ABC ≌ △DCB

∴∠EBC=∠ECB

∵∠AEB=∠EBC+∠ECB ∠EBC=∠ECB ∠AEB=50°

∴∠EBC=25°