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数学
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如图,在四边形ABCD中,AC平分∠BAD,过C作CE⊥AB于E,并且
AE=
1
2
(AB+AD)
,求∠ABC+∠ADC的度数.
人气:333 ℃ 时间:2019-08-16 19:10:53
解答
过C作CF垂直AD于F,∵AC平分∠BAD,∴∠FAC=∠EAC,∵CE⊥AB,CF⊥AD,∴∠DFC=∠CEA=90°,∴△AFC≌△AEC(AAS),∴AF=AE,CF=CE,∵AE=12(AB+AD),∴2AE=AB+AD,又∵AD=AF-DF,AB=AE+BE,AF=AE,∴2AE=AE+BE+AE...
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