(1)证明:∵AD是△ABC的角平分线, ∴∠1=∠2, ∵EF⊥AD于P, ∴∠1+∠AEP=90°,∠APE=∠APF=90°, ∴∠AEP=∠AFP, ∵∠AFP=∠CFM, ∴∠CFM=∠AEP, ∵∠ACB=90°, ∴∠M+∠CFM=90°, ∴∠M+∠AEP=90°, ∴∠M=∠1;
(2)证明:∵EF⊥AD,AD平分∠BAC, ∴∠1=∠2,∠APE=∠APF=90°, 又∵∠AEF=180°-∠1-∠APE,∠AFE=180°-∠2-∠APF, ∴∠AEF=∠AFE, ∵∠CFM=∠AFE, ∴∠AEF=∠AFE=∠CFM, ∵∠AEF=∠B+∠M,∠MFC=∠ACB-∠M, ∴∠B+∠M=∠ACB-∠M,即∠M=(∠ACB-∠B). |