如圖，若∠CAE=45°，PA=5，PC=1，則BC=?

∠CAE = 45°
∠ACE = 180° - ∠CAE - ∠AEC = 180° - 45° - 90° = 45°
∴ AE = CE ( 等角對邊相等 )

∵ ΔAPE ~ ΔCPD ( AAA )
AE / CD = AP / CP
CE / CD = PA / PC
CD / CE = PC / PA = 1 / 5

∵ ΔPCD ~ ΔBCE ( AAA )
PC / BC = CD / CE = PC / PA = 1 / 5
1 / BC = 1 / 5
BC = 5