???$解：可能$???
???$因?yàn)檎叫蜛BCD的邊長(zhǎng)為2 ， AE=EB $???
???$所以AD=2 ， AE=1$???
???$所以DE=\sqrt{AD2+AE2}=\sqrt{5}$???
???$①當(dāng)△AED∽△CMN時(shí)，$???
???$\frac {AE}{CM}=\frac {DE}{MN}$???
???$因?yàn)锳E=1，DE=\sqrt{5}，MN=1$???
???$所以\frac {1}{MN}=\frac {\sqrt{5}}{1}$???
???$所以CM=\frac {\sqrt{5}}{5}$???
???$②當(dāng)△AED∽△CNM時(shí)，$???
???$\frac {AD}{CM}=\frac {DE}{MN}$???
???$AD= 2，DE=\sqrt{5}，MN = 1$???
???$所以\frac {2}{CM}=\frac {\sqrt{5}}{1}$???
???$所以CM=\frac {2\sqrt{5}}{5}$???
???$綜上所述，相似時(shí)CM的長(zhǎng)為\frac {\sqrt{5}}{5}或\frac {2\sqrt{5}}{5}$???
