Question

what is the missing reason in the proof? statements reasons 1. ∠1 = ∠2 1. given 2. ∠1 ≅ ∠4 2. vertical angles are congruent. 3. ∠2 ≅ ∠4 3.? 4. a || b 4. if two lines and a transversal form congruent corresponding angles, then the lines are parallel.

Explanation:

Step1: Recall transitive property

The transitive property of congruence states that if $\angle A\cong\angle B$ and $\angle B\cong\angle C$, then $\angle A\cong\angle C$. Here, since $\angle 1\cong\angle 2$ (given) and $\angle 1\cong\angle 4$ (vertical - angles are congruent), we can conclude that $\angle 2\cong\angle 4$ by the transitive property of congruence.

Answer:

Transitive property of congruence