Prove that if a transversal intersects two parallel lines then each pair of alternate interior angles are equal and also prove its converse.
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Alternate interior angles are formed when a transversal passes through two lines. The angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.These pairs are alternate interior angles.
Another way to think about alternate interior angles is by using the z-pattern. Notice that the pair of alternate interior angles makes a Z.

In this window pane (see video), angle a and angle b are alternate interior angles because they are on opposite sides of the transversal but inside the parallel lines.
Alternate Interior Angles Theorem
The Alternate Interior Angles theoremstates, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
A theorem is a proven statement or an accepted idea that has been shown to be true. The converse of this theorem, which is basically the opposite, is also a proven statement: if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
These theorems can be used to solve problems in geometry and to find missing information. This diagram shows which pairs of angles are equal and alternate interior. Notice that the lines are parallel.
Another way to think about alternate interior angles is by using the z-pattern. Notice that the pair of alternate interior angles makes a Z.

In this window pane (see video), angle a and angle b are alternate interior angles because they are on opposite sides of the transversal but inside the parallel lines.
Alternate Interior Angles Theorem
The Alternate Interior Angles theoremstates, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
A theorem is a proven statement or an accepted idea that has been shown to be true. The converse of this theorem, which is basically the opposite, is also a proven statement: if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.
These theorems can be used to solve problems in geometry and to find missing information. This diagram shows which pairs of angles are equal and alternate interior. Notice that the lines are parallel.
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