Alternate Interior Angles Theorem

They lie on the inner side of the parallel lines but the opposite sides of the transversal.

Alternate interior angles theorem. Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. For example in the following figure α must be equal to x y. Alternate angles are the four pairs of angles that.

Alternate interior angles theorem proof. Have distinct vertex points lie on opposite sides of the transversal and. A very important consequence of the angle sum property of triangles is the exterior angle theorem.

Here we have a new pair of lines parallel and crossed by a transversal. So in the figure below if k l then 2 8 and 3 5. If the two angles of one pair are congruent equal in measure then the angles of each of the other pairs are also congruent.

The alternate exterior angles theorem states that if a pair of parallel lines are cut by a transversal then the alternate exterior angles are congruent. 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 angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles are equal.

The proof of this theorem is straightforward. The theorem says that when the lines are parallel the alternate interior angle is equal. Alternate interior angles theorem the alternate interior angles theorem states if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent.

An exterior angle in any triangle is equal to the sum of the opposite interior angles. Once you can recognize and break apart the various parts of parallel lines with transversals you can use the alternate interior angles theorem to speed up your work. Answer the alternate interior angles theorem states that when two parallel lines are cut by a transversal the resulting alternate interior angles are congrue.