如图,AE平行BC,AD,BD平分角EAB,角CBA,EC过点D,求证角EAB等于AB等于AE+BC

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如图,AE平行BC,AD,BD平分角EAB,角CBA,EC过点D,求证角EAB等于AB等于AE+BC
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如图,AE平行BC,AD,BD平分角EAB,角CBA,EC过点D,求证角EAB等于AB等于AE+BC
如图,AE平行BC,AD,BD平分角EAB,角CBA,EC过点D,求证角EAB等于AB等于AE+BC

如图,AE平行BC,AD,BD平分角EAB,角CBA,EC过点D,求证角EAB等于AB等于AE+BC
证明:延长AD和BC相交于点F
∵AE平行BC
∴∠EAD=∠BFD
又AD平分角EAB,则∠EAD=∠BAF
∴∠BAF=∠BFD
∴AB=BF,又BD平分角CAB,则∠BAD=∠DBF
∴AD=DF.而∠ADE=∠CDF
∴△ADE≌△CDF
∴AE=CF
∴AB=AE+BC