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

##### 1 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.

#### 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