Properties of Parallel Lines

What special situations are created when parallel lines are crossed by a transversal?

Whenever parallel lines are crossed by a transversal, we can more easily determine relationships between (and sometimes values of) the angles formed by those crossings.  In turn, we can use those special relationships to prove whether the lines crossed by the transversal are parallel.  We can use the converse (the logical opposite) of each postulate or theorem to prove whether the lines are parallel.

Same-Side Interior Angles Postulate

If a transversal intersects two parallel lines, then the same-side interior angles formed are supplementary.

·         Converse: If two same-side interior angles are supplementary, then the lines they sit between are parallel.