Question

given: ( g parallel h ) and ( angle 2 cong angle 3 )
prove: ( e parallel f )

statements	reasons
2. ( angle 1 cong angle 2 )	2. corresponding angles theorem
3. ( angle 2 cong angle 3 )	3. given
4. ( angle 1 cong angle 3 )	4. transitive property
5. ( e parallel f )	5. ?

Explanation:

Step1: Recall the converse of corresponding angles theorem

The converse of the 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.

Step2: Identify the angles and lines

We have $\angle 1 \cong \angle 3$ (from step 4) and these are corresponding angles formed by the transversal cutting lines $e$ and $f$.

Step3: Apply the converse of corresponding angles theorem

Since $\angle 1 \cong \angle 3$ (corresponding angles) and they are formed by the transversal intersecting lines $e$ and $f$, by the converse of the corresponding angles theorem, we can conclude that $e \parallel f$.

Answer:

To complete the proof:

Statements	Reasons

So the final step is to state \( e \parallel f \) with the reason being the converse of the corresponding angles theorem.