looked everywhere an coulndn't find the meaning and an example
what is the consecutive interior angles converse
The consecutive interior angles converse is used to prove that two lines crossed by a transversal are parallel. (Usually you are given two parallel lines; this is the "converse" because you are given two lines and have to prove that they are parallel.)
The consecutive interior angles converse states that If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
If you can show that angles inside the two lines and on the SAME side of the transversal are supplementary (add to 180 degrees) than you can conclude the lines are parallel.
Hope this helps!