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