题目内容
如图,梯形ABCD中,AD∥BC,AB=3,BC=4,连结BD,∠BAD的平分线交BD于 点E,且AE∥CD,则AD的长为( )
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A.1 | B.2 | C.3 | D.4 |
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A.
试题分析:延长AE交BC于F,
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∵AE是∠BAD的平分线,
∴∠BAF=∠DAF,
∵AD∥CB,
∴∠DAF=∠AFB,
∴∠BAF=∠AFB,
∴AB=BF,
∵AB=3,BC=4,
∴CF=4-3=1,
∵AD∥BC,AE∥CD,
∴四边形AFCD是平行四边形,
∴AD=CF=1.
故选A.
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