Alternate Interior Angles Are Congruent

Proving alternate interior angles are congruent the same the alternate interior angles theorem states that if two parallel straight lines are intersected by a third straight line transversal then the angles inside between the parallel lines on opposite sides of the transversal are congruent identical.

Alternate interior angles are congruent. 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. 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. A d and b c.

So in the figure below if k l then 2 8 and 3 5. Formally alternate interior angles are two interior angles which lie on different parallel lines and on opposite sides of a transversal. Therefore by the definition of congruent angles m 1 m 5.

Therefore the alternate angles inside the parallel lines will be equal. These angles are called alternate interior angles. The alternate interior angles theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congruent.

This is illustrated in the image below. Alternate exterior angles are congruent. Alternate exterior angles are located on opposite sides of the transversal and are diagonal from one another.

Outside the bun in order to help visualize the difference between exterior and. In the above given figure you can see two parallel lines are intersected by a transversal. Alternate interior angles are congruent.

These angles are congruent.