Question

1. complete the flow proof of the converse of the corresponding angles theorem. fill in the blanks. given: ∠2≅∠3 prove: c || d ∠2≅∠3 given ∠1 = ∠2 transitive prop. of ≅ converse of the corr. ∠s thm.

Explanation:

Step1: Identify vertical - angle relationship

$\angle1\cong\angle2$ (Vertical angles are congruent)

Step2: Use the transitive property

Since $\angle2\cong\angle3$ (given) and $\angle1\cong\angle2$, by the transitive property of congruence, $\angle1\cong\angle3$.

Step3: Apply the converse of corresponding - angles theorem

If corresponding angles are congruent, then the lines are parallel. Since $\angle1$ and $\angle3$ are corresponding angles and $\angle1\cong\angle3$, we can conclude that $c\parallel d$.

Answer:

The missing statement in the flow - proof is $\angle1\cong\angle2$ (Vertical angles are congruent) and the reasoning for the last step is "If corresponding angles are congruent, then the lines are parallel".