C=∠1+∠2=∠B+∠CР∴∠B=∠1Р∴AD//BCР课堂检测:Р1.证明:∵AB//DCР∴∠D=∠B,∠C=∠AР∵OA=OBР∴∠A=∠BР∴∠C=∠DР∴OC=ODР2.证明:∵AD//BCР∴∠ADB=∠DBCР∵BD平分∠ABCР∴∠ABD=∠DBCР∴∠ABD=∠ADBР∴AB=ADР1.∠B=∠C=∠CAD=∠BAD,∠CAB=∠CDA=∠BDAРAB=AC=BD=AD=CDР2.证明:Р∵CE//DAР∴∠CEB=∠AР∵∠A=∠BР∴∠B=∠CEBР∴CE=BEР∴△CEB是等腰三角形Р3.解:等腰三角形Р证明:∵AB=AC,Р∴∠ABC=∠ACB,Р又∵BD和CD分别是∠ABC和∠ACB的平分线Р∴∠DBC= ∠ABC,∠DCB=∠ACB,Р∴∠DBC=∠DCB,Р∴△DBC为等腰三角形.Р4.解:∵四边形ABCD是矩形,Р∴AD∥BC,Р∴∠1=∠2,Р∵沿矩形ABCD的对角线BD翻折△ABD得△A′BD,Р∴△ABD≌△A′BD,Р∴∠2=∠3,Р∴∠1=∠3,Р∴BF=DF,Р∴△BDF是等腰三角形.Р5.解:(1)∵∠A=70°Р∴∠ABC+∠ACB=110°Р∵CD、BD平分∠BCA及∠ABCР∴∠DBC+∠DCB=55°Р∴∠BDC=125°Р(2)∵EF//BCР∴∠EDB=∠DBC,Р∵BD平分∠ABCР∴∠DBC=∠DBEР∴∠DBE=∠EDBР∴BE=DE,同理可知:DF=FCР∴EF=ED+DF=EB+FCР6.(1)证明:∵AD是∠BAC的平分线РDE⊥AB,DF⊥ACР∴DE=DFР∴∠DEF=∠DFEР(2)在Rt△ADE和Rt△ADF中РDE=DFРAD=ADР∴Rt△ADE≌Rt△ADF(HL)Р∴AE=AFР(3)∵AE=AFР∴点A在EF的垂直平分线上Р∵ED=FDР∴点D在EF的垂直平分线上Р∴AD垂直平分EF
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