题目

如图，∠ABC=90°，D、E分别在BC、AC上，AD⊥DE，且AD=DE. 点F是AE的中点，FD的延长线与AB的延长线相交于点M，连接MC. (1)求证：∠FMC=∠FCM； (2)AD与MC垂直吗？说明你的理由. 答案：解：（1）证明：∵△ADE是等腰直角三角形，F是AE的中点. ∴DF⊥AE，DF=AF=EF. ··············································································· 1分 又∵∠ABC=90°，∠DCF、∠AMF都与∠MAC互余， ∴∠DCF=∠AMF. ·······························�The people there are (friend) to me.