Question

1. abc is a triangle 1. given
2. y || z 2. given
3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3.?
4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅
5. m∠1 + m∠2 + m∠3 = m∠lam 5. ∠ addition postulate
6. m∠1 + m∠2 + m∠3 = 180° 6. def. straight angle
7. m∠5 + m∠2 + m∠6 = 180° 7. substitution

which could be the missing reason in step 3?
alternate interior angles are congruent
alternate exterior angles are congruent
vertical angles are congruent
corresponding angles are congruent

Explanation:

We know that when two parallel lines ($y\parallel z$) are cut by a transversal, angles in corresponding positions are congruent. $\angle1$ and $\angle5$ as well as $\angle3$ and $\angle6$ are in corresponding positions with respect to the parallel lines $y$ and $z$ and the transversals forming the triangle. Alternate - interior angles are inside the two parallel lines and on opposite sides of the transversal, which is not the case here. Alternate - exterior angles are outside the two parallel lines and on opposite sides of the transversal, which is not applicable either. Vertical angles are formed by two intersecting lines, not relevant in this parallel - line and transversal context.

Answer:

corresponding angles are congruent