# What is the converse of the Alternate Interior Angles Theorem?

##### 1 Answer

Converse of the Alternate Interior Angles Theorem:

*If alternate interior angles formed by two lines with an intersecting traversal are congruent
then these two lines are parallel.*

#### Explanation:

Let's recall the Alternate Interior Angles Theorem.

*If two lines are parallel
then alternate interior angles formed by these two lines with an intersecting traversal are congruent.*

The above figure illustrates this theorem that can be symbolically expressed as

or

Here the premise of a theorem is

*two lines are parallel*.

The conclusion is

*alternate interior angles formed by these two lines with an intersecting traversal are congruent.*

**Converse** theorem is the one obtained by taking a conclusion as a premise of a theorem and a premise - as conclusion.

So, it would look like this:

*If alternate interior angles formed by two lines with an intersecting traversal are congruent
then these two lines are parallel.*

Using the same figure above, this converse theorem can be symbolically expressed as

or