ΔABC ~ ΔBDC ~ ΔADB 




1) ∠ABC= 90  1) Given  
2) BD ⊥ AC  2) Given  
3) ∠BDC = ∠BDA = 90^{0}  3) By definition of perpendicular  
4) ∠ABD + ∠DBC = 90  4) Since ∠ABC = 90  
5) ∠C + ∠DBC + 90 = 180  5) Angle sum property  
6) ∠C + ∠DBC = 90  6) By subtraction property  
7) ∠C = ∠ABD  7) From (4) and (7)  
8) ΔADB ~ Δ BDC  8) By AA postulate ( from 3 and 7) 

9) ∠ADB = ∠ABC  9) Each 90^{0}  
10) ∠A = ∠A  10) Reflexive (common angle)  
11) ΔADB ~ ΔABC  11) By AA postulate (from 9 and 12) 

12) ∠C = ∠C  12) Reflexive (common angle )  
13) ΔBDC ~ ΔABC  13) By AA postulate ( from 11 and 12) 

14) ΔADB ~ Δ BDC  14) from (3) and (7)  