There are some special properties of parallel lines and intersecting lines. The most fundamental aspects of the Geometry emerge from these concepts. Such lines show the relationship between the angles formed.

Parallel Lines

Parallel lines are the lines in the same plane that, if extended to infinity, would never intersect.

parallel-lines

The angles formed by the intersection of a line with two parallel lines have some interesting properties.

Intersecting Lines

When lines intersect, the measures of the angles on opposite sides of the intersection are equal; these angles are called vertical angles. All of the angles labeled x have equal measures, and all of the angles labeled y have equal measures.

The measures of the angles on the same side of a line, represented as x and y, must add up to 180 degrees; these are called supplementary angles.

intersecting-lines

When parallel lines are cut by a transversal, three important angle relationships are formed.

transversal