What is a Line

In order to understand what a perpendicular bisector is, we should start with the very basics. Take a look at the definition below.

Definition
Line A one-dimensional element that is straight

 

A line is the very basic unit of any shape. It is one dimensional because it only has one dimension: length. When you draw a line, it is drawn with two arrows at each end.

 

line_definition

 

This means that the line extends to infinity in both directions. Keep in mind that infinity is endless.

The best Maths tutors available
Intasar
4.9
4.9 (36 reviews)
Intasar
£48
/h
Gift icon
1st lesson free!
Paolo
4.9
4.9 (29 reviews)
Paolo
£30
/h
Gift icon
1st lesson free!
Jamie
5
5 (16 reviews)
Jamie
£25
/h
Gift icon
1st lesson free!
Harinder
5
5 (16 reviews)
Harinder
£15
/h
Gift icon
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£30
/h
Gift icon
1st lesson free!
Petar
4.9
4.9 (12 reviews)
Petar
£40
/h
Gift icon
1st lesson free!
Shane
5
5 (24 reviews)
Shane
£25
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (31 reviews)
Sehaj
£25
/h
Gift icon
1st lesson free!
Intasar
4.9
4.9 (36 reviews)
Intasar
£48
/h
Gift icon
1st lesson free!
Paolo
4.9
4.9 (29 reviews)
Paolo
£30
/h
Gift icon
1st lesson free!
Jamie
5
5 (16 reviews)
Jamie
£25
/h
Gift icon
1st lesson free!
Harinder
5
5 (16 reviews)
Harinder
£15
/h
Gift icon
1st lesson free!
Matthew
5
5 (17 reviews)
Matthew
£30
/h
Gift icon
1st lesson free!
Petar
4.9
4.9 (12 reviews)
Petar
£40
/h
Gift icon
1st lesson free!
Shane
5
5 (24 reviews)
Shane
£25
/h
Gift icon
1st lesson free!
Sehaj
4.9
4.9 (31 reviews)
Sehaj
£25
/h
Gift icon
1st lesson free!
Let's go

What is a Line Segment

Line segments are usually what people think about when they imagine lines. Let’s take a look at the definition of a line segment.

 

Definition
Line Segment A one-dimensional element that is a straight line between two points and doesn’t go beyond these two points

 

You can also think of a line segment as a specific part of a line. Take a look below.

 

line_segment

 

As you can see, we have two points A and B on a line that, by definition, extends to infinity in both directions. However, there is still part of that line between the points A and B, which we call a line segment. Below is the notation for a line segment.

 

Notation
Line Segment overline{AB}

 

The notation for a line segment is simply the two points or name of the line with a straight line over it. Lines are usually written as one or two capital letters:

 

Notation Example
Name of the line 1 capital letter L
Two points of the line 2 capital letters overline{AB}

 

Parallel Lines

When we talk about lines, we usually are referring to either line segments or two other types of lines. These lines are parallel and perpendicular lines. In order to understand what perpendicular lines are, let’s see what parallel lines are first.

 

Definition
Parallel lines Lines that are always the same distance from each other and never cross, or intersect

 

These are the properties that all parallel lines have, regardless of whether they are lines or line segments. Let’s take a look at the notation for parallel lines.

 

Notation
Parallel lines overline{line ; 1} ; perp ; overline{line ; 2}

 

Here is an example of two parallel line segments and lines.

 

parallel_notation

 

Let’s take a look at the notation for these parallel lines.

Notation
A overline{AB} ; perp ; overline{CD}
B overline{L} ; perp ; overline{M}

 

What are Perpendicular Lines

Now that you understand the basics of lines, we can now define perpendicular lines. To be perpendicular means that two lines intersect, or cross, at a 90 degree angle.

 

 

As you can see, two lines are perpendicular when the four angles they produce form 90 degree angles. In the table below, you will see the notation for perpendicular lines.

On lines Written
Squares at the angles overline{AB} ; perp ; overline{CD}

 

Slope Test for Perpendicular Lines

Now that you have seen what perpendicular lines are, you may be wondering - is there a way to test whether or not two lines are perpendicular? The easiest way is to check to see if the angle is 90 degrees.

 

If you don’t know the angle, you can use the slope test. When two lines are perpendicular, they have reciprocal slopes. See the example below.

 

[

frac{3} = frac{1}{3}

]

 

What Does Congruent Mean?

Another important concept related to perpendicular lines is called congruency. This can refer to lines, shapes and even three dimensional objects. Let’s focus on lines and line segments.

 

When two lines are congruent, it means that they have the same length. Take a look at the notation below.

 

[

overline{AB} ; cong ; overline{CD}

]

 

Another way to tell whether two lines are congruent is when they have dash marks on them of the same number.

 

What is Perpendicular Bisector

A perpendicular bisector is another way in which two lines can interact with each other. Perpendicular bisectors refer to two perpendicular lines.

 

What’s special about perpendicular bisectors is that the lines bisect each other. Bisect, in maths, means that the line or shape is divided exactly in half.

 

This means that each bisected line is congruent to each other when two lines are perpendicular bisectors.

 

Perpendicular Bisector Theorem

The perpendicular bisector theorem is a continuation of the idea of perpendicular bisectors. Imagine two perpendicular lines overline{AB} ; cong ; overline{CD} .

 

Say you draw a point on overline{CD} above the intersection point. If you were to connect that point to the end of the line overline{AB} on either side, both of these lines would have the same length.

 

In other words, this drawn point would be equidistant to the endpoints of overline{AB}.

 

Circumcentre of a Triangle

Imagine you have a triangle. Take one side of that triangle and draw a line that is perpendicular to it. If you repeat this three times, you have each side of the triangle and the lines that are perpendicular to each of those sides.

 

These lines all intersect at one point inside of the triangle. This point of intersection is called the circumcentre of the triangle.

 

Circumcircle

Now that you know what the circumcentre of a triangle is, imagine that the circumcentre is now the centrepoint of a circle. This circle, at the same time, touches each of the three points of the triangle.

 

This circle is called a circumcircle.

>

The platform that connects tutors and students

Did you like this article? Rate it!

1 Star2 Stars3 Stars4 Stars5 Stars 5.00 (1 rating(s))
Loading...

Danica

Located in Prague and studying to become a Statistician, I enjoy reading, writing, and exploring new places.