^_ ^

geometry is not my friend : (

explain and show work

Well starting with just the first statement b is congruent to c by vertical... yes. because they are formed by the intersection and non adjacent.  so A and C are still okay.

answer choice B on the other hand b is congruent to h by corresponding that is not true.. one they are not corresponding and two they are supplementary because they are same side exterior angles.  so you can eliminate B.

now the next line in answer choice a.. c and e are supplementary by ss interior... yes that is correct. 
now the next line in answer choice c.. d and h are supplementary.. that is wrong.. d and h are corresponding and therefore are congruent so you can eliminate answer choice C.

just checking the rest.. e and h are congruent by vertical.. correct.. and finally substitution to finish the proof.  So A is the correct proof.