Question

PLEASE HELP (look at pictures)

Answer 1

Answer:

This is a theorem called Converse of Alternate Exterior Angles that states that if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,

1.  

Reason: Given  

Statement: $\angle1\cong\angle2$

2.  

Reason: Def of vertical $\angle s$

Statement: $\angle1\:and\:\angle3 \ are \ vertical$

3.  

Reason: Def of vertical $\angle s$

Statement: $\angle1\cong\angle3$  

4.

Reason: Transitive Property

Statement: $\angle2\cong\angle3$

5.  

Reason: corresponding Angles Converse Postulate

Statement: $p\parallel q$