How are corresponding angles defined?

Corresponding angles are defined as angles that are on the same side of the transversal and in corresponding positions relative to the two parallel lines. When a transversal intersects two parallel lines, it creates several pairs of angles. Each pair consists of one angle from each parallel line that occupies the same relative position.

For example, if one angle is in the upper left corner and the other angle is also in the upper left corner on the opposite parallel line, they are corresponding angles. The key characteristic is that they are on the same side of the transversal and occupy similar positions, making them congruent when the lines are parallel. This understanding of corresponding angles is essential in geometry, particularly when working with parallel lines and transversals, as it aids in proving relationships between angles and establishing geometric properties.