Parallel, Perpendicular and Intersecting Lines

What are parallel lines?

Parallel lines are lines in a plane that are always the same distance apart and never meet, no matter how far they are extended. They have the same slope if represented in a coordinate system.

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees). In a coordinate system, the slopes of two perpendicular lines are negative reciprocals of each other (i.e., if one line has a slope of m, the other line will have a slope of −1/m​).

What are intersecting lines?

Intersecting lines are lines that meet or cross at one point. Unlike parallel lines, intersecting lines have different slopes unless they are the same line (coincident).

What is the significance of the slopes in determining the relationship between lines?

The slope of a line indicates its steepness and direction. Comparing the slopes of two lines helps determine their relationship:

• Same slope: The lines are parallel.
• Negative reciprocal slopes: The lines are perpendicular.
• Different slopes: The lines will intersect at some point unless they are parallel

Can two lines be both parallel and perpendicular?

No, two lines cannot be both parallel and perpendicular. Parallel lines never intersect and have the same slope, while perpendicular lines intersect at a right angle and have slopes that are negative reciprocals of each other.

Parallel, Perpendicular and Intersecting lines are three types of lines based on their properties. This article provide worksheet for practice of questions based on parallel, perpendicular and intersecting lines. This article also contain, formula and solved examples to make you understand how to solve the worksheet