The proof abc ≅ dcb that is shown.

given: a ≅ d; cd||ab
prove: abc ≅ dcb

what is the missing reason in the proof?

alt. ext. s are ≅
asa
aas
corr. int. s are ≅

The correct answer is:

AAS

Explanation:

AAS stands for "angle-angle-side."  This states that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

In these triangles, we have ∠CAB ≅ ∠CDB given to us to begin with.  Throughout the proof, we find that ∠ABC ≅ ∠DCB.  We also have that CB is congruent to itself.  This is two angles and a side not included, so this is AAS.