Question

given: \\( \angle 1 \cong \angle 2 \\) prove: \\( p \parallel q \\) assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Vertical angles are congruent

$\angle1\cong\angle3$

Step2: Transitive property of congruence

Since $\angle1\cong\angle2$ (given) and $\angle1\cong\angle3$, then $\angle2\cong\angle3$

Step3: If alternate - interior angles are congruent, then lines are parallel

If $\angle2\cong\angle3$, then $p\parallel q$

Answer:

Statements	Reasons
$\angle2\cong\angle3$	Transitive property of congruence ($\angle1\cong\angle2$ (given) and $\angle1\cong\angle3$)
$p\parallel q$	If alternate - interior angles are congruent, then lines are parallel ($\angle2\cong\angle3$)