Key Points

When two or more lines cross each other in a plane, they are called intersecting lines. They meet at a single common point, and at this point of intersection, four angles are formed.

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays, forming a straight line. The sum of the angles in a linear pair is always $180^{\circ}$.

When two lines intersect, they form two pairs of vertically opposite angles. The angles in each pair are directly opposite to each other and are always equal in measure.

Two lines are said to be perpendicular to each other if they intersect at a right angle. This means all four angles formed at the intersection are equal to $90^{\circ}$.

Parallel lines are two lines in the same plane that never intersect, no matter how far they are extended in either direction. The perpendicular distance between them is always constant.

A transversal is a line that intersects two or more lines at distinct points. When a transversal intersects two lines, it forms eight angles.

Corresponding angles are located in the same relative position at each intersection where a transversal crosses two lines. If the two lines are parallel, then corresponding angles are equal.

Alternate interior angles are a pair of angles on opposite sides of the transversal and between the two lines. If the two lines are parallel, then alternate interior angles are equal.

These are pairs of angles on the same side of the transversal and between the two lines. If the two lines are parallel, these angles are supplementary, which means their sum is $180^{\circ}$.

If a transversal intersects two lines such that any pair of corresponding angles is equal, then the two lines are parallel.

If a transversal intersects two lines such that any pair of alternate interior angles is equal, then the two lines are parallel.

If a transversal intersects two lines such that any pair of interior angles on the same side of the transversal are supplementary (add up to $180^{\circ}$), then the two lines are parallel.