Alternate Interior Angles Proof

The transversal crosses through the two lines which are coplanar at separate points.

Alternate interior angles proof. A proof of the common geometric theorem showing that when lines are parallel alternate interior angles are congruent. In this video we are discussing proof of the theorem if two lines are intersected by a transver. They lie on the inner side of the parallel lines but the opposite sides of the transversal.

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. Alternate interior angles theorem proof. So in the figure below if k l then 2 8 and 3 5.

Proof and definition of alternate and exterior angles with a transversal and parallel lines. If the two lines are parallel then the alternate interior angles are congruent. If you are looking for other proofs ch.

So let s do exactly what we did when we proved the alternate interior angles theorem but in reverse going from congruent alternate angels to showing congruent corresponding angles. The alternate angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles are equal. This video is the 9th part of the topic lines and angles.

Assume l and m are parallel and prove that alternate interior angles are congruent. Then l and m are parallel if and only if alternate interior angles of the intersection of l and t and m and t are equal. Suppose that l m and t are distinct lines.