1)
1) ∠3 ≅ ∠7 , lines parallel a and b
Theorem:
"If two lines are intercepted by a transversal and alternate interior angles
are congruent, then the lines are parallel"
In this theorem, we have 2 alternate interior angles ∠3 , ∠7 that's why we apply this.
2) ∠9 ≅ ∠11 (Corresponding angles)
Postulate:
"Given that two lines are intercepted by a transversal and corresponding angles are congruent, then the lines are parallel."
3) ∠2 ≅ ∠16 (Alternate Exterior Angles)
From these Alternate exterior angles, comes the Alternate Exterior angles theorem:
"Given that two parallel lines are cut by a transversal, the alternate exterior angles are congruent."
4) m∠5 +m∠12 = 180º
Collateral angles are supplementary
"Given that two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel"
This is also valid for collateral angles since ∠5 and ∠12 are collateral angles and ∠12 ≅ ∠6.