What Is a Perpendicular? In geometry, it’s a key concept that describes when two lines meet to form a perfect right angle. Understanding perpendicular lines helps students visualize shapes, measure angles correctly, and build a strong foundation for topics like coordinate geometry, design, and construction.
What is a Perpendicular?
In mathematics, perpendicular lines are two intersecting lines with a 90° angle. The angle created when two lines cross one another to generate a perpendicular line should be 90° (right angle).
The term “perpendicular to all points in the plane” or “perpendicular to each line it intersects” is used to describe a line that is perpendicular to the plane. If the dihedral angle at which two planes intersect is a right angle, then the two planes are said to be perpendicular in space.
The symbol “⊥” stands for perpendicular lines. If two lines l1 and l2 are perpendicular to one another and meet at 90 degrees, they are denoted as l1⊥l2. And the foot of the perpendicular refers to the intersection’s position.
Properties of a Perpendicular Line
The appearance of perpendicular lines has previously been demonstrated. If a figure has an “L” form, the vertex’s angle corresponds to a right angle. All crossing lines are not necessarily perpendicular to one another, but perpendicular lines always cross each other. Perpendicular lines have two key characteristics.
- In every case, perpendicular lines cross or intersect.
- Any two perpendicular lines will always intersect at an angle of 90 degrees.
The formula for Perpendicular Lines
To determine if the two provided lines are perpendicular to one another or not, apply the formula of the perpendicular line. Once we have the slope of the two lines we wish to compare, we can use the formula of the perpendicular line. Two lines that are perpendicular to one another form a 90-degree angle.
The slopes of the two lines are m1 and m2.
For any two lines with equations y = m1x+c1, and y = m2x+c2, the formula to recognize that these two lines are perpendicular is:
m1m2 =-1 or m1=-1m2
Perpendicular vs Parallel lines
In contrast to perpendicular lines, no matter how far apart they are from one another and how much they may stretch in any direction, two straight lines are considered to be parallel if they never cross. Look at the lines below to notice the distinction between parallel and perpendicular lines.
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Parallel Lines |
Perpendicular lines |
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Lines that are always the same distance apart and have no points of intersection are said to be parallel. |
Perpendicular lines are those that cross at a right angle to one another. |
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the opposing sides of a rectangle and the steps of a straight staircase. |
the letter “L”; the corner of two walls |
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Two parallel lines are represented by this symbol: || |
The symbol used to indicate two perpendicular lines: ⊥⊥. |
How to Draw Perpendicular Lines?
All we need to draw a perpendicular line is a scale (ruler), a compass, or a protractor. We will go through step-by-step instructions for drawing perpendicular lines with a protractor and a compass. Thus, there are two ways to create perpendicular lines to a given line.
Using a protractor
In arithmetic, a protractor is regarded as a crucial measuring tool in the geometry toolbox. This tool is useful for creating perpendicular lines as well as measuring angles in degrees. Follow the instructions below to create a perpendicular line at point P on the supplied line.
- Step 1: Let A be the given point on the given line m
- Step 2: Align the protractor such that its center is on A and its baseline is on line m.
- Step 3: Draw a line from point B to the protractor’s 90-degree line.
- Step 4: Trace a line across points A and B. Then, m ⊥ line n at A.
Using a Compass
A compass can be used to draw a perpendicular line as well. The procedures shown below can be used to create a perpendicular line at point P on a line.
- Step 1: Set the compass needle on the designated point A. Then, on either side of the specified location, draw an arc with the proper radius.
- Step 2: Make the compass broader. A tiny arc should be drawn above the indicated line using the compass tip on the new points. The two new arcs will cross each other.
- Step 3: Join points A and B where the arcs overlap using the ruler.
FAQs
1. When do children learn perpendicular lines in primary school?
Children learn about a quarter, half, and full turns in Key Stage 1. To assist students in grasping different turns, teachers frequently ask students to stand up and face various directions.
Children will learn in Year 3 that two lines that are perpendicular to one another are referred to as perpendicular lines. Additionally, they will learn that a right angle is a quarter- or 90-degree turn. Every child should be able to recognize right angles in polygons.
2. Do perpendicular lines have to cross each other?
These lines usually come together at an angle.
3. What distinguishes parallel and perpendicular lines from one another?
Parallel lines never overlap; instead, they run parallel to one another and do so at right angles (90°).
4. Are all lines crossed one another perpendicularly?
No, intersecting lines are not always parallel to one another. Various than at a 90-degree angle, they may also intersect at other angles.
Conclusion
For children to comprehend what perpendicular lines are, they should first grasp the concept of right angles.
Children may struggle to understand angles, so it might be helpful to have them stand up and do quarter, half, and full turns during their time in primary school to ensure they are aware that a quarter turn is 90 degrees, a half turn is 180 degrees, and a full turn is 360 degrees. If you are planning to teach your kids about this essential topic, you can make your own collections of perpendicular worksheets using our worksheet maker.
