解:∵$A B \perp A C, ∠B=45° \text {, } $
∴$∠A C B=45° \text {, } $
∵$A D //B C \text {, } $
∴$∠D A C=∠A C B=45° \text {, } $
∵$A D \perp D C \text {, } $
∴$∠A C D=90°-45°=45° \text {, } $
∴$∠A C D=∠C A D \text {, } $
∴$A D=C D=2 \mathrm{cm} \text {, } $
$\text { 在Rt } \triangle A D C \text { 中, } A C=\sqrt{2^{2}+2^{2}}=2 \sqrt{2}(\mathrm{cm}), $
∵$∠A C B=∠B \text {, } $
∴$A C=A B=2 \sqrt{2} \mathrm{cm} \text {, } $
$\text { 在Rt } \triangle A B C \text { 中, } B C=\sqrt{(2 \sqrt{2})^{2}+(2 \sqrt{2})^{2}}=4(\mathrm{cm}) . $
