2014年临沂市中考数学试卷及答案word版(14)

∵GM=GC+MC=AD+MC， ∴AM=AD+MC. ······································································································· （4分） 方法四：

连接ME并延长交AD的延长线于点N， ∵∠MEC＝∠NED， EC＝ED， ∠MCE＝∠NDE=90°， ∴△MCE≌△NDE. ∴MC=ND，∠CME=∠DNE. ··················································································· （2分） 由方法一知△EFM≌△ECM， ∴∠FME=∠CME， ∴∠AMN=∠ANM. ···································································································· （3分） ∴AM=AN=AD+DN=AD+MC. ················································································ （4分） （2）（本小问5分）

D 成立. ···················································· （1分） 方法一：延长CB使BF=DE，

连接AF，

E ∵AB=AD，∠ABF=∠ADE=90°，

∴△ABF≌△ADE， ∴∠FAB=∠EAD，∠F=∠AED. ··········· （2分）

C F B M ∵AE平分∠DAM， ∴∠DAE=∠MAE.

∴∠FAB=∠MAE， ∴∠FAM=∠FAB+∠BAM=∠BAM+∠MAE=∠BAE. ·················································· （3分） ∵AB∥DC， ∴∠BAE=∠DEA， ∴∠F=∠FAM， ∴AM=FM. ··············································································································· （4分） 又∵FM=BM+BF=BM+DE， ∴AM=BM+DE. ······································································································· （5分） 方法二：

设MC=x，AD=a.

由（1）知 AM=AD+MC=a+x. 在Rt△ABM中，

∵AM2 AB2 BM2，

∴(a x)2 a2 (a x)2， ······················································································ （3分）

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