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1.3 探索三角形全等的条件(4)1. ∵ AB ∥ CD,∴ ∠ABE = ∠CDF.
∵ AE ⊥ BD,CF ⊥ BD,
∴ ∠AEB = ∠CFD = 90°.
在△ABE和△CDF中,
∵ ∠ABE = ∠CDF,∠AEB = ∠CFD,
AE = CF,
∴ △ABE ≌ △CDF(AAS). ∴ AB = CD.
2. ∵ △ABC ≌ △DCB,
∴ AB = DC,∠A = ∠D.在△AOB和△DOC中,
∵ ∠A = ∠D,∠AOB = ∠DOC,AB = DC,
∴ △AOB ≌ △DOC(AAS).