Question

1. what is the missing statement in the following proof?

given: \\( \angle 1 \cong \angle 2 \\)
prove: \\( l \parallel m \\)
\\( \angle 1 \cong \angle 3 \\)
vertical \\( \angle s \\) are \\( \cong \\).
\\( \angle 3 \cong \angle 2 \\)
transitive property of \\( \cong \\)
\\( l \parallel m \\)
corres. \\( \angle s \\) are \\( \cong \\).

Explanation:

Step1: Analyze the proof structure

The proof uses the transitive property of congruence ($\angle3\cong\angle2$) which requires two congruent angle pairs. One pair is $\angle1\cong\angle3$ (vertical angles) and the other pair should be given.

Step2: Recall the given information

The problem states "Given: $\angle1\cong\angle2$". This is the missing statement that, along with $\angle1\cong\angle3$, allows the use of the transitive property to get $\angle3\cong\angle2$.

Answer:

$\angle1\cong\angle2$