Question

given: ( g parallel h ) and ( angle 2 cong angle 3 ) prove: ( e parallel f ) what is the missing reason in the proof? converse alternate interior angles theorem alternate exterior angles theorem converse corresponding angles theorem vertical angles theorem

Explanation:

Step1: Analyze the relationship between angles and lines

We know that $\angle1\cong\angle3$ (from step 4). The converse corresponding angles theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Here, lines $e$ and $f$ are cut by a transversal, and $\angle1$ and $\angle3$ are corresponding angles.

Step2: Apply the theorem

Since $\angle1\cong\angle3$, by the converse of the corresponding angles theorem, we can conclude that $e\parallel f$.

Answer:

converse corresponding angles theorem