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) 