Question

given: \\( \angle 1 \cong \angle 2 \\) prove: \\( p \parallel q \\) correct! assemble the next statement.

Explanation:

Step1: Identify the relationship between angles and lines

We know that if two corresponding angles are congruent, then the two lines are parallel.

Step2: Analyze the given congruent angles

We have \(\angle2\cong\angle3\) (from previous steps: \(\angle1\cong\angle2\) (given), \(\angle1\cong\angle3\) (vertical angles theorem), then \(\angle2\cong\angle3\) by transitive property). \(\angle2\) and \(\angle3\) are corresponding angles.

Step3: Apply the converse of corresponding angles theorem

If \(\angle2\cong\angle3\), then by the converse of the corresponding angles theorem, \(p\parallel q\).

Answer:

Statements: \(p\parallel q\)
Reasons: converse of corresponding angles theorem