Alternate Interior Angles Theorem Triangles

The theorem states that if a transversal crosses the set of parallel lines the alternate interior angles are congruent.

Alternate interior angles theorem triangles. The alternate angles theorem states that if two parallel lines are cut by a transversal then each pair of alternate interior angles are equal. When lines crossed by the transversal are parallel you can use the alternate exterior angles theorem to know the. Interior alternating angles and exterior alternating angles are congruent that is they have the same measure of the angle.

If two parallel lines are cut by a transversal then the alternate interior angles are equal. Converse of the alternate interior angles theorem 1 m 5 m 3 given 2 m 1 m 3 vertical or opposite angles 3 m 1 m 5 using 1 and 2 and transitive property of equality both equal m 3 4 1 5 3 the definition of congruent angles 5 ab cd converse of. Alternate angle theorem states that when two parallel lines are cut by a transversal then the resulting alternate interior angles or alternate exterior angles are congruent.

So in the figure below if k l then 2 8 and 3 5. Alternate interior angles theorem proof. Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

They lie on the inner side of the parallel lines but the opposite sides of the transversal. 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. The alternate interior angles theorem states that if two parallel lines are cut by a transversal then the pairs of alternate interior angles are congruent.

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. The transversal crosses through the two lines which are coplanar at separate points. Now that you have gone through this lesson carefully you are able to recall that angles on opposite sides of a transversal and outside two lines are called alternate exterior angles.

4 5 and 3. 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.