GIVEN: <2 congruent to <3 PROVE: m is parallel to n

Answer 1

You really haven't supplied enough of the question to answer here for sure, but I can infer that there is a diagram that goes with this. Also I am guessing you are using the < symbol for "angle" since there's no angle symbol on the keyboard. (It can be found on the web, here it is for you to copy and paste somewhere to save: ∠ )

Now from what I am inferring there might be a line with to lines passing through it at the same angle, and some two angles are labeled ∠2 and ∠3. To prove two lines are parallel you need to prove that corresponding angles are congruent. (In case you're not sure what corresponding angles means, imagine 10th street crosses Paul Avenue and Ortega Road. If I'm standing on the northwest corner of 10th and Ortega and you are standing on the northwest corner of 10th and Paul, we are standing on corresponding corners. Got it? And congruent means the same. Like equal, but for shapes and angles.)

I will assume ∠2 and ∠3 are not corresponding or the problem would be done already. You need to use another rule of geometry, for example the Rule of Opposite Angles to prove that corresponding angles are equal. Opposite angles are what that sounds like. When two lines cross there are four angles. Two angles next to each other are adjacent (and they always add up to 180°) and two that are not next to each other are opposite and they are always equal to each other.

Sorry I can't help you more. If you can describe the diagram next time it would help.