Alternate Interior Angles Converse Theorem

Converse of the alternate interior angles theorem.

Alternate interior angles converse theorem. The converse of this theorem which is basically the opposite is also a proven statement. 3 m 1 m 5 using 1 and 2 and transitive property of equality both equal m 3. So it would look like this.

5 ab cd converse of the. Thus the converse of alternate interior angles theorem is proved. How to prove of the converse of the alternate interior angles theorem.

Converse alternate interior angles theorem states that if two lines and a transversal form alternate interior angles that are congruent then the two lines are parallel. This video shows a proof of the alternate interior angle converse. Since the corresponding angles of the lines ab and cd are equal the lines are parallel.

Converse theorem is the one obtained by taking a conclusion as a premise of a theorem and a premise as conclusion. Li l i and on o n with transversal h e h e given lar arn l a r a r n given lar h ai l a r h a i vertical. This time we can use the alternate exterior angles theorem to state that the alternate exterior angles are congruent.

To prove the converse if two lines are cut by a transversal and the alternate interior angles are congruent then the lines are parallel we work the other way around. 2 m 1 m 3 vertical or opposite angles. If two lines are cut by a transversal and the alternate interior angles are congruent then the lines are.

The converse of the alternate exterior angles theorem is also true. Since k l by the corresponding angles postulate 1 5. Therefore by the definition of congruent angles m 1 m 5.