Question

Please help thank you very much.

Answer 1

2) Corresponding angles of parallel lines cut by a transversal are congruent.

3) Vertical angles are congruent.

4) Transitive Property. If angle 2 is congruent to angle 6 and angle 4 is congruent to 2, then angle 6 is congruent to angle 4.

Answer 2

Proofs are great!

We are given that two lines, l and n are parallel, which gives us a lot angles that we can work with.
The first statement says that 2 and 6 are congruent, and this is so by the Corresponding Angles Theorem, which states that if two lines are cut by a transversal, their corresponding angles (angles in a row of one side of the transversal) are congruent.
The second statement states that 4 is congruent to 2, which is so by the Vertical Angles Theorem, which states that two angles that are opposite each other that are cut by a transversal are congruent.
The third statement says that 6 is congruent to 4, which is by the Alternate Interior Angles Theorem, which states if a line is cut by a transversal, then the angles opposite of each other that are inside the transversal are congruent.

Hope this helps!

:)