Given: ∠1 ≅ ∠2
Prove: a ∥ b

What is the missing statement in the proof?

∠1 ≅ ∠2

a ⊥ b

a ∥ b

∠1 ≅ ∠4

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.