QED D. Showing Statements are Equivalent Let P and Q be statements. When both statements are valid, we say P and Q are logically equivalent statements. Sometimes more than two statements are logically equivalent. To prove P, Q, R, and S are all logically equivalent it is necessary to show that any one implies any other. Several schemes can be used.
P means proving the four separate implications shown.
Once these are done all others are easy to see. All the following statements are equivalent. If two parallel lines are cut by a transversal then interior angles on the same side of the transversal are supplementary. Let l,m be parallel lines and t a transversal making alternate interior angles a and b as shown below. Let P be intersection of t and m.