Question

Alternate interior angles are congruent, then the lines are parallel. Is this statement true or false, and why?

Answer 1

This is a great question! :3 First, if you have taken Geometry in high school (or in some cases middle school like I did) you will remember that there are dozens of important postulate and theorems. Now for simplicity's sake, the theorem that applies to your question is this: Parallel Lines Theorem: If two parallel lines are cut by a transversal, then corresponding angles are congruent, alternate interior angles are congruent, and alternate exterior angles are congruent. I will attach an image that represents an example of two alternate interior angles so you can visualize it. The transversal between the two parallel lines is what makes the two alternate interior angles congruent, without the lines being parallel, the two angles would be different degrees. All you need to know is that theorem I wrote above, and after you have memorized it, it becomes accepted knowledge and much simpler, trust me! I'm so sorry for rambling, I hope I didn't confuse you more than helping, if you still have a question feel free to ask! :)