Alternate Interior Angles
One of the important properties of parallel lines intersected by a transversal is the relationship between alternate interior angles.

Definition
Alternate interior angles are a pair of angles that lie on opposite sides of the transversal and inside the two lines. When the two lines are parallel, alternate interior angles are congruent, meaning they have the same measure.

Explanation
When two parallel lines are intersected by a transversal, such as a line that crosses two other lines, alternate interior angles are formed. These angles are located on the inside of the two parallel lines and on opposite sides of the transversal.

Relationship
The key relationship to remember is that alternate interior angles are congruent when the two lines are parallel. This property can be used to solve for unknown angles in geometric problems involving parallel lines and transversals.

Example
For example, if two parallel lines are intersected by a transversal and one of the angles measures 50 degrees, then the alternate interior angle on the other side of the transversal will also measure 50 degrees. This relationship holds true for any pair of alternate interior angles when the lines are parallel.
Remembering the properties of alternate interior angles can help in solving geometric problems involving parallel lines and transversals.