Math CSET II How to Prove Two Lines Are Parallel

One popular question that continues to pop up on the math CSET II is proving two lines are parallel. This may happen when the two lines are floating in space or when they are cut by a transversal. Since it is the CSET test they will not just directly ask you (satanists) but rather bury what you actually need to find within a Russian doll of a question. If you do figure out that what you need to prove is two lines are parallel here are the most straight forward ways.

Two lines floating in space

Image result for parallel lines

Prove they are parallel by:

  • Showing the two lines have the same slope, use y=mx+b form and prove both slopes are equal.
  • Showing the distance between the two lines is the same FOREVER.  In other words for any two points on the line, using distance formula, the distance will be equal.
  • Showing the two lines never intersect.
  • Getting frustrated and saying “Because I said.”  It is the prevailing logic of the 8 year old in my house so who knows.

Two lines cut by a transversal

This means there are two seemingly parallel lines and then a third line cutting through them.  In the diagram below a and b are the “maybe parallel” lines and t is the transversal.

Image result for transversal

Prove a and b are parallel by:

  • Showing corresponding angles are equal. 
  • Showing alternate interior angles are equal
  • Showing alternate exterior angles are equal
  • Showing same side interior angles are supplementaryparallel lines transversal proof

Any of of these by themselves proves the two lines are parallel.  You do not have to show all of them.  

Stay parallel my friends.

 

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