如图,已知△ABC中,∠ACB=90°,ACDE和BCFG都是正方形,过D,E,F,G各点作直线AB的垂线,垂足分别为D1,E1,F1,G1求证（1）AE1=BG1(2)EE1+GG1=AB(3)DD1+FF1=E1G1

Question

如图,已知△ABC中,∠ACB=90°,ACDE和BCFG都是正方形,过D,E,F,G各点作直线AB的垂线,
垂足分别为D1,E1,F1,G1
求证（1）AE1=BG1
        (2) EE1+GG1=AB
       (3) DD1+FF1=E1G1

Answer 1

证明：(1)过C点作CC1⊥AB,垂足为C1,则△AEE1≌△CAC1,△BGG1≌△CBC1,所以AE1＝CC1＝BG1；(2)由(1)得EE1＝AC1,GG1＝BC1,所以EE1+GG1＝AC1+BC1＝AB；(3)连DF,则△DCF≌△ACB,设DF交CC1的反向延长线于H,∠FDC＝∠BAC＝...