3.(2012•嘉兴)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=50°,求∠EBC的度数?
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![3.(2012•嘉兴)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=50°,求∠EBC的度数?](/uploads/image/z/1692670-22-0.jpg?t=3%EF%BC%8E%EF%BC%882012%26%238226%3B%E5%98%89%E5%85%B4%EF%BC%89%E5%A6%82%E5%9B%BE%2C%E2%96%B3ABC%E4%B8%8E%E2%96%B3DCB%E4%B8%AD%2CAC%E4%B8%8EBD%E4%BA%A4%E4%BA%8E%E7%82%B9E%2C%E4%B8%94%E2%88%A0A%3D%E2%88%A0D%2CAB%3DDC%EF%BC%8E%EF%BC%881%EF%BC%89%E6%B1%82%E8%AF%81%EF%BC%9A%E2%96%B3ABE%E2%89%8CDCE%EF%BC%9B%EF%BC%882%EF%BC%89%E5%BD%93%E2%88%A0AEB%3D50%C2%B0%2C%E6%B1%82%E2%88%A0EBC%E7%9A%84%E5%BA%A6%E6%95%B0%3F)
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3.(2012•嘉兴)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=50°,求∠EBC的度数?
3.(2012•嘉兴)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=50°,求∠EBC的度数?
3.(2012•嘉兴)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=50°,求∠EBC的度数?
∵∠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°