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Pairs Of Lines

Pairs of lines can relate to each other in four different ways: intersecting lines, parallel lines, perpendicular lines and skew lines. These concepts are useful for understanding and solving various geometry problems.

Intersecting Lines

Intersecting lines are lines that meet at a point. When two lines intersect, they define angles at the point of intersection.

at point C

The following video gives a definition of intersecting lines.

Parallel Lines

Parallel lines are lines that never intersect. The distance between the two lines is fixed and the two lines are going in the same direction.

Two parallel lines
can be written as

The following video gives a definition of parallel lines.

Perpendicular Lines

Perpendicular lines are lines that intersect at one point and form a 90° angle.

Two perpendicular lines
can be written as

The following video gives a definition of perpendicular lines.

Skew Lines

The above relationships between lines take place on the same plane. However, skew lines only happen in space. Skew lines never intersect because they are not on the same plane. Skew lines are difficult to draw because they exist in the three dimensional space. Lets consider a cube.

Imagine the lines running
along the edges of a cube as shown, and line running on the front surface of the cube.

They are lines in different planes and will never intersect.

The following video gives a definition of skew lines.

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