As shown in the figure, AC ⊥ CB, BD ⊥ CB, ab = DC, verify ∠ abd = ∠ ACD

As shown in the figure, AC ⊥ CB, BD ⊥ CB, ab = DC, verify ∠ abd = ∠ ACD

prove:
∵AC⊥CB,BD⊥CB
∴∠ACB=∠DBC=90°
∴AB=DC,BC=CB
∴△ABC≌△DCB
∴∠DCB=∠ABC
∵∠ACB=∠DBC=90°
∴∠ABD=∠ACD