Question

1. what is the missing statement in the proof?

given: ∠1 ≅ ∠2
prove: l || m
∠1 ≅ ∠2
given
∠1 ≅ ∠3
vertical ∠s are ≅.
transitive property of ≅
l || m
corres. ∠s are ≅.
∠1 ≅ ∠2
l || m
∠3 ≅ ∠2
∠1 ≅ ∠3

Explanation:

Step1: Recall the transitive property of congruence

The transitive property states that if \(a\cong b\) and \(b\cong c\), then \(a\cong c\). Here, we know \(\angle1\cong\angle2\) (given) and \(\angle1\cong\angle3\) (vertical angles are congruent).

Step2: Apply the transitive property

By the transitive property of congruence, if \(\angle1\cong\angle2\) and \(\angle1\cong\angle3\), then \(\angle3\cong\angle2\).

Answer:

\(\angle3\cong\angle2\) (the third option)