(1)由∠ADB=∠ACB+90°,又∠ADB=∠ADE+90°,所以∠ADE=∠ACB;
由AC*BD=AD*BC得AC:AD=BC:BD,又等腰三角形中ED=BD,所以AC:AD=BC:ED;
所以三角形ABC∽三角形AED,且AC:AD=BC:ED=AB:AE,角CAB=角DAE.
(2)由角CAB=角DAE,且角CAB=角CAD+角BAD,角DAE=角BAE+BAD,所以角CAD=角BAE;
由AC:AD=BC:ED=AB:AE,得AC:AB=AD:AE.
所以三角形ACD∽三角形ABE.得AC:AB=AD:AE=CD:BE.
(3)在等腰直角三角形BDE中,由勾股定理得BE=√2*BD;
由AC:AB=CD:BE得AC:AB=CD:√2*BD,即AB*CD/AC*BD==√2