Whats the difference between converse of alternate interior angle theorem and alternate interior angle theorem?

Question

Claire Akin · Accepted Answer

Consider two statements:
(A) Two lines that are cut by a transversal are parallel
(B) Alternate interior angle formed by these lines are congruent
They are equivalent.
See below for explanation.

Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent. Let's represent it in a form "if A then B": If two lines that are cut by a transversal are parallel [Part A] then alternate interior angles formed by these lines are congruent [Part B]. Converse theorem should look like "if B then A": If alternate interior angles formed by these lines are congruent [Part B] then two lines that are cut by a transversal are parallel [Part A]. So, these are two different theorems, each requiring its own proof. But, since both theorem #A->B# and #B->A# can be proven independently, both statement are equivalent. If one is true, another is as well, if one if false, another is well.

Savannah Aguilar · Answer

undefined The converse of the alternate interior angle theorem states that if two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel. The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.