Proving 2 lines are parallel (Geometry tidbits)

As your child is progressing through the geometry class, he/she will be asked to provide proofs to state whether 2 lines are parallel or not.  I have compiled the basic 4 theorems/postulates that will determine if 2 lines are parallel or not.  Since this is their first time endeavoring into providing proofs to justify a hypothesis, it should be noted that more practices will be needed in order to get better at this type of proofs.

My personal belief is that the proof portion of geometry is just something that the students will need to endure through the geometry curriculum.  As students progressed into higher math, they will be asked to recall facts and how to calculate angles and lengths of geometric shapes.  It is quite seldom that they will be asked to prove that 2 lines are parallel.  Instead they normally will be told that 2 lines are parallel and angle A is 63 degrees, and be asked to find another angle B.

Without further adieu, the 4 basic theorems are summarized below (with the "cheat sheet" below)

1. Corresponding angles converse

• If 2 lines are cut by a transversal so that the corresponding angles are congruent, then the 2 lines are parallel.
  

• If 2 lines are cut by a transversal so that the alternate interior angles are congruent, then the 2 lines are parallel.
  

• If 2 lines are cut by a transversal so that the consecutive interior angles are supplementary (they added to 180 degrees), then the 2 lines are parallel.
  

• If 2 lines are cut by a transversal so that the alternate exterior angles are congruent, then the 2 lines are parallel.