Question

complete the two - column proof
given: ( overline{sj}paralleloverline{pg},angle scongangle p,overline{sj}congoverline{pg},overline{sg}congoverline{pj} )
prove: ( \triangle sjgcong\triangle pgj )

1. ( overline{sj}congoverline{pg},overline{sg}congoverline{pj} ) 1) given
2. ( overline{gj}congoverline{jg} ) 2) reflexive property of congruence
3. ( angle scongangle p ) 3) given
4. ( overline{sj}paralleloverline{pg} ) 4) given
5. ( angle sjgcongangle pgj ) 5)

Explanation:

Step1: Recall properties of parallel lines

When two lines are parallel (\(SJ\parallel PG\)), the alternate interior angles are congruent.

Step2: Identify the angles

\(\angle SJG\) and \(\angle PGJ\) are alternate interior angles formed by the transversal \(JG\) intersecting the parallel lines \(SJ\) and \(PG\).

Answer:

Alternate interior angles of parallel lines are congruent.