Postulates and Theorems of Parallel Lines
First, we need to know what type of angles are <3 and <7. Following the definition:
If two lines are crossed by another line, the angles in matching corners are called Corresponding Angles.
Angles 3 and 7 are corresponding angles and they are told to be congruent.
Now we apply the postulate that reads:
The Converse of the Corresponding Angles Postulate. If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
The postulate that can be used to prove that the lines are parallel is The Converse of the Corresponding Angles Postulate