已知:如图,在菱形ABCD中,E、F分别是BC、CD上的点,且CE=CF.

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已知:如图,在菱形ABCD中,E、F分别是BC、CD上的点,且CE=CF.

公主 影儿

发布日期:2010-05-16 15:30:37

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已知:如图,在菱形ABCD中,EF分别是BCCD上的点,且CE=CF

1)求证:△ABE≌△ADF

2)过点CCGEA,交AFH,交ADG,若∠BAE=25°,∠BCD=130°,求∠AHC的度数.









公主 赵敏

发布日期:2010-05-16 15:29:36


解:(1) 因为四边形ABCD为菱形

所以AB=AD ∠B=∠D BC=CD

又EC=CF

所以BE=BC-EC DF=DC-FC

即BE=DF

所以△ABE≌△ADF

(2) 因为∠BCD=130° 所以∠BAD=130°

又△ABE≌△ADF 所以∠BAE=∠DAF=25°

所以∠EAF=∠BAD-2∠BAE=130°-50°=80°

因为AE平行CG,所以∠AHG=∠EAH=80

所以

 
公主 赵敏

发布日期:2010-05-16 15:30:37


所以 ∠AHC=180°-∠AHG=100°