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- Two lines are termed as parallel if they lie in the same plane, are the same distance apart, and never meet each other. Perpendicular lines are intersecting lines that always meet at an angle of 90°.
www.cuemath.com/geometry/parallel-and-perpendicular-lines/Parallel and Perpendicular Lines - Definition, Properties ...
- What Are Parallel and Perpendicular lines?
- Definition of Parallel and Perpendicular Lines
- Equations of Parallel and Perpendicular Lines
- Solved Examples on Parallel and Perpendicular Lines
Parallel and perpendicular lines are two important concepts in geometry. Parallel lines are the lines that never intersect each other. Thus, two parallel lines always maintain a constant distance between them. Perpendicular lines are the two lines that intersect each other at a right angle. We come across examples of parallel lines and perpendicula...
Parallel and perpendicular lines play a vital role in geometry. Both of them have distinct properties and applications.
We represent a straight line through an equation y=mx+cwhere “m” represents the slope of the line and c is the y-intercept. Two parallel lines never intersect each other and have the same steepness, so their slopes are always equal. Consider two lines y=2x–1 and y=2x+3. We can see that both the equations have the same slope, 2. In mathematical term...
1. Which triangle has perpendicular lines in it? Solution: Right-angled triangle has perpendicular lines in it. 2. If the slope of one of the two parallel lines is 5, then what will be the slope of the other parallel line? Solution: m1=5 We know that the slopes of two parallel lines are equal, i.e., m1=m2. So, m2=5. 3. Find the slopes of the lines ...
Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees). Two nonvertical lines in the same plane, with slopes \(m_{1}\) and \(m_{2}\), are perpendicular if the product of their slopes is \(−1: m1⋅m2=−1\).
a vertical line is parallel to another vertical line. a vertical line is perpendicular to a horizontal line (and vice versa). Summary. parallel lines: same slope; perpendicular lines: negative reciprocal slope (−1/m)
- Slope
- −0.5
- Railway Tracks. Embark on a mental journey along a railway track, where parallel lines stretch into the distance as far as the eye can see. These tracks never converge, remaining equidistant from each other throughout their course.
- Window Frames. Take a closer look at the windows of a building or your own home. Notice the elegant pattern formed by the vertical and horizontal lines of the window frames.
- Pedestrian Crosswalks. Picture yourself at a bustling intersection, where safety and order are maintained by the bold lines painted on the ground. The parallel lines of the crosswalk extend ahead, providing a safe path for pedestrians.
- Skyscrapers and Streets. Imagine standing in the heart of a metropolis, surrounded by towering skyscrapers and bustling streets. Take note of how these structures align themselves harmoniously.
Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. (They also point in the same direction). Just remember: Always the same distance apart and never touching. The red line and blue line are parallel in both these examples: Example 1. Example 2. Try it yourself: Perpendicular to Parallel.
As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular.
