Statements

Reasons

1) AD = DC 
1) Given 
2) BD = DE 
2) By construction 
3) ∠ADB = ∠CDE 
3) Vertically opposite angles 
4) ΔADB ≅ ΔCDE 
4) By SAS postulate 
5) EC = AB and ∠CED = ∠ABD 
5) CPCTC 
6) CE  AB 
6) If alternate interior angles are congruent then the lines are parallel 
7) ∠ABC + ∠ECB = 180 
7) Angles formed on the same side of transveral are supplementary. 
8) 90 + ∠ECB = 180 
8) Since ∠B = 90 given 
9) ∠ECB = 180 90 = 90 
9) By subtraction property 
10) AB = EC 
10) From (5) 
11) BC = CB 
11) Reflexive (Common side) 
12) ∠ABC = ∠ECB 
12) Each 90^{0}

13) ΔABC ≅ ΔECB 
13) SAS postulate 
14) AC = BE 
14) CPCTC 
15) 1/2AC = 1/2BE ⇒ 1/2AC = BD 
15) Multiply by 1/2 but 1/2BE = BD by mid point definition. 