The missing statement in the proof is ∠1 ≅ ∠4.
Solution:
(1) Given ∠1 ≅ ∠2
(2) ∠1 and ∠4 are vertical angles.
Vertical angle theorem:
If two angles are vertically opposite then they are congruent.
By vertical angle theorem,
⇒ ∠1 ≅ ∠4
(3) Transitive property of congruence:
If A = B and B = C, then A = C.
From (1) and (2), ∠2 ≅ ∠4.
(4) If two lines and a transversal form congruent corresponding angles, then the lines are parallel.
Therefore line a || line b.
⇒ a || b.
Hence the missing statement in the proof is ∠1 ≅ ∠4.
