Online Math Center

Math Geometry: The Line

Do you know what’s the next simplest geometrical figure after the point? It’s a straight, infinite geometrical figure. It’s the line! Compared to the point which has no dimensions, the line is one-dimensional.

What is the use of the line in geometry?

When a line has two ends it is called a line segment or side-line and we usually use line segments to name the sides of the triangle. When a line has just one end, it is called a “ray”.

Lines are part of any geometrical shape and plane, that’s why it is important to know the basics about lines.

Math Symbols Related To The Line

“ ↔ “ – this symbol represents the infinite line; usually is noted above two letters to symbolize that the line on which the two points are, is an infinite line, example: 

AB

“ ⎻ “ – a simple line above two letters indicates a line segment, which starts at point A and ends at point B:

the line in geometry

“→” – this symbol indicates a ray, which starts from point A;

 

the line in geometry

“∠” – this symbol indicates an angle formed by two rays, example: ∠ABC = 30°

 

“⟂” – this symbol indicates that two lines are perpendicular, thus forming a 90° angle. The notation would look like this:

the geometric line

“ ∥ “ – this symbol indicates that two lines are parallel to each other: 

geometrical lines

When two lines are not parallel, we would use the “∦” symbol. When two lines are parallel and equal, we use the symbol “⋕” . 

Types of Lines

In geometry, there are a variety of lines that relate to spatial relationships between points or angles. It’s pretty simple to memorize the type of each line, so here we go: 

Vertical line

A vertical line is a straight line that goes from top to bottom.

geometrical line

Horizontal line

A horizontal line is a straight line that goes from left to right. 

geometric line

Parallel lines

Two or more lines that do not intersect at any point, infinitely, are called parallel lines.

parallel lines in geometry

Perpendicular lines

Two straight lines that meet at an intersection point and form a right angle (90°) are called perpendicular lines. 

Perpendicular Lines

Oblique lines

These lines are diagonal or slanting lines.

Oblique Lines

Diagonal or oblique lines can be perpendicular or parallel.

Skew Lines

When it comes to spatial geometry, two non-parallel lines that are not intersecting in a given space are called skew lines. 

Skew Lines

Concurrent lines

In our past article, we mentioned concurrency in points. Since two or more lines can cross through a common concurrent point, these lines are also called concurrent.  

Concurrent Lines

Transversal lines

The line that cuts two or more straight lines is called a transversal line. The cut lines are not necessarily parallel. 

Transversal Lines

Coplanar lines

Coplanar lines are straight lines that exist in the same spatial plane.

The Rules Of Lines In Math

1. When a transversal line intersects/cuts two parallel lines:
  • Alternate angles are equal.
  • Corresponding angles are equal.
2. The sum of the angles on a straight line is 180º, while the sum of the angles formed at a point is 360º.

3. When 2 straight lines intersect, they form vertically opposite and equal angles.

Remember the above simple and short line rules and get ready to apply them in daily life. Did you know that line calculations are an important part of computer graphics and architecture? 

Let’s PRACTICE!

Solve the following exercises:

 

#1. Look at the image below and choose which option is true.

math line problem
Statement: The straight lines AB and CD are:

2. are not parallel because the two given corresponding angles are not equal

3. are parallel lines

4. are not parallel because the two given alternate angles are not equal

5. are not parallel because the two given consecutive interior angles do not add to 180°

 

#2. Look at the image below and choose which option is true. 

math line problem
Statement: The straight lines ST and UV are parallel, then the angles c and e are:

1. consecutive interior angles

2. corresponding angles

3. alternate interior angles

4. vertical angles

 

#3. Check out the image below: 

math line problem
The two parallel lines A and B are cut by a transversal line. If ∠5 = 70°, find the measure of the following angles: ∠7, ∠9, ∠10.

 

#4. Check out the image below and then choose the correct option from the statements below:

math line problem

1. Angles 2 and 6 are examples of vertical / corresponding angles. 

2. Angles 1 and 8 are examples of alternate interior / exterior angles. 

3. The angle that is corresponding to angle 8 is angle 3 / 4

4. If lines m and n are parallel, then angles 3 and 6 / 8 have equal measures.

If you want to memorize the types of lines better, you can always solve some online exercises, here.When it comes to solving geometry problems, practice does indeed help you become better at mathematics. 

For more fun exercises on lines, you can check out these questions. Additionally, if you want to learn more about 4th-grade mathematics, our OMC tutors offer individual and group lessons that turn any student into a math champion!

Reach out to us and meet our OMC math tutors! 

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