Formal proof
Statement Reason
ΔABC is a right triangleBD ⊥ AC Given
∠ ABC = ∠BDC Right angles have the same measure.
∠ BCA = ∠ BCD same angle
ΔABC ~ΔBDC AA Similarity Postulate
BC
DC
=
AC
BC
Corresponding sides of similar triangles are proportional
BC2 = (AC)(DC) Cross multiplication
∠ ABC = ∠ADB Right angles have the same measure
∠ BCA = ∠ BAD same angle
ΔABC ~ΔABD AA Similarity Postulate
AB
AD
=
AC
AB
Corresponding sides of similar triangles are proportional
AB2 = (AC)(AD) cross multiplication
AB2 + BC2 = (AC)(AD) + (AC)(DC) Addition
AB2 + BC2 = (AC)(AD + DC) ?
AB2 + BC2 = (AC)2 Addition

What is the missing reason?
A) Addition Property
B) Division Property
C) Associative Property
D) Distributive Property