Alternate Interior Angles Theorem

Statement for alternate interior angles.

Alternate interior angles theorem. These angles are called alternate interior angles. The alternate interior angles theorem states if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent. Malcolm has a master s degree in education and holds four teaching certificates. A theorem is a proven statement or an.

We need to prove that angle 4 angle 5 and angle 3 angle 6. In today s lesson we will prove the alternate interior theorem stating that interior alternating angles and exterior alternating angles between parallel lines are congruent. Alternate interior angle theorem the alternate interior angles theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congruent. The alternate interior angle theorem states that if a transversal crosses the set of parallel lines then the alternate interior angles are congruent.

Notice the pairs of blue and pink angles. The angles which are formed inside the two parallel lines when intersected by a transversal are equal to its alternate pairs. Alternate interior angles definition. In the above given figure you can see two parallel lines are intersected by a transversal.

Interior alternating angles and exterior alternating angles are congruent that is they have the same measure of the angle. Apply the alternate interior angles theorem and its converse to find angles in parallel lines crossed by a transversal and to prove lines parallel instructor. The theorem states that if a transversal crosses the set of parallel lines the alternate interior angles are congruent. The angles that are formed on opposite sides of the transversal and inside the two lines are aias.

Alternate interior angles theorem proof. So in the figure below if k l then 2 8 and 3 5. Line a is parallel to line b.