There are four theorems. Let's list all of them, highlighting the

hypothesis

and

conclusion .

Corresponding Angles Theorem If t w o p a r a l l e l l i n e s a r e c u t b y a t r a n s v e r s a l, then t h e p a i r s o f c o r r e s p o n d i n g a n g l e s a r e c o n g r u e n t

Alternate Interior Angles Theorem If t w o p a r a l l e l l i n e s a r e c u t b y a t r a n s v e r s a l, then t h e p a i r s o f a l t e r n a t e i n t e r i o r a n g l e s a r e c o n g r u e n t

Alternate Exterior Angles Theorem If t w o p a r a l l e l l i n e s a r e c u t b y a t r a n s v e r s a l, then t h e p a i r s o f a l t e r n a t e e x t e r i o r a n g l e s a r e c o n g r u e n t

Consecutive Interior Angles Theorem If t w o p a r a l l e l l i n e s a r e c u t b y a t r a n s v e r s a l, then t h e p a i r s o f c o n s e c u t i v e i n t e r i o r a n g l e s a r e s u p p l e m e n t a r y

The converse of a conditional statement,

q \to p,

exchanges the hypothesis and the conclusion of the conditional statement.

Corresponding Angles Converse If t w o l i n e s a r e c u t b y a t r a n s v e r s a l s o t h a t the corresponding angles are congruent, then t h e l i n e s a r e p a r a l l e l

Alternate Interior Angles Converse If t w o l i n e s a r e c u t b y a t r a n s v e r s a l s o t h a t the alternate interior angles are congruent, then t h e l i n e s a r e p a r a l l e l

Alternate Exterior Angles Converse If t w o l i n e s a r e c u t b y a t r a n s v e r s a l s o t h a t the alternate exterior angles are congruent, then t h e l i n e s a r e p a r a l l e l

Consecutive Interior Angles Converse If t w o l i n e s a r e c u t b y a t r a n s v e r s a l s o t h a t the consecutive interior angles, are supplementary then t h e l i n e s a r e p a r a l l e l

All of these converses are true.

Exercise