Types of Lines in Math
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Types of Lines in Math
In this lesson, you will learn
- the difference between straight lines and curved lines
- the difference between a line, a line segment and a ray
- how to recognize vertical, horizontal, diagonal, perpendicular and zigzag lines
- what wavy, closed curved, dotted, dashed and spiral lines are
Straight Lines and Curved Lines
Basically, there are two different types of lines in mathematics and generally these are straight lines and curved lines.
Is a spiral line a straight line or a curved line?
Show answer
A curved line. A spiral keeps bending as it winds around its center, so no part of it is straight.
Line, Line Segment and Ray
In math, a line goes on forever in both directions. That is why the lines in the pictures in this lesson have arrows at both ends. A line through the points A and B is called line AB.
Line segment
A line segment is a part of a line with two endpoints. It does not go on forever: it stops at both ends. A line segment with the endpoints A and B is called line segment AB.
Ray
A ray is a part of a line with one endpoint. It starts at the endpoint and goes on forever in one direction. A ray that starts at A and goes through B is called ray AB.
Count the endpoints: a line has no endpoints, a ray has one endpoint, and a line segment has two endpoints.
The edge of a ruler starts at one end and stops at the other. Is it more like a line, a line segment or a ray?
Show answer
A line segment. It has two endpoints, so it does not go on forever.
Types of Lines Made with Straight Lines
There are five different types of lines that can be made with straight lines and these are vertical line, horizontal line, diagonal line, perpendicular lines, and zigzag line.
Vertical line
A vertical line is a line that goes straight up and down, from top to bottom or from bottom to top.
Horizontal line
A horizontal line is a line that has a slope of zero. In other words, if you walk on a horizontal line, you will never feel that you are going up. Not even a tiny bit!
Diagonal line
A diagonal line is neither vertical nor horizontal.
A diagonal line is also called an oblique line or a slanted line.
Perpendicular lines
When a horizontal line meets a vertical line, you end up with perpendicular lines.
Perpendicular lines are lines that meet at a right angle (90°). A horizontal line and a vertical line always meet at a right angle.
Parallel lines are lines that never meet, because they always stay the same distance apart, like the two rails of a train track.
Thinking that only a horizontal line and a vertical line can be perpendicular. Two diagonal lines are also perpendicular when they meet at a right angle, like a plus sign turned on its side.
Zigzag line
A zigzag line is made of short straight lines that keep changing direction, up and down, like a row of letter Zs.
Staircase line
A staircase line is also made with straight lines. It goes across, then up, then across, then up again, like the steps of a staircase. Each turn is a square corner.
- Look at the long line on the left side of the E. It goes straight up and down, so it is a vertical line.
- Look at the three short lines at the top, middle and bottom. They are flat, so they are horizontal lines.
- Each horizontal line meets the vertical line at a square corner (a right angle), so each one is perpendicular to the vertical line.
- All four lines are straight; the E has no curved lines.
The letter E uses one vertical line and three horizontal lines that are perpendicular to it.
The letter T is made of which type of lines?
Show answer
Perpendicular lines. The T is a horizontal line that meets a vertical line at a right angle.
Types of Curved Lines
Wavy line
A wavy line is a curved line that goes up and down smoothly, like a wave in the sea. It is like a zigzag line with round tops instead of sharp points.
Closed curved line
A closed curved line is a curved line that ends where it begins, so it has no ends at all. A circle and an oval are closed curved lines. The curved line near the top of this lesson is an open curved line, because it does not join up with itself.
Is the letter O an open curved line or a closed curved line?
Show answer
A closed curved line. It ends where it begins, so it has no ends.
Dotted, Dashed and Spiral Lines
Lines can also be formed with dashes and dots. If the line is made with dots, it is called a dotted line and if it is made with dashes, it is called a dashed line.
Last but not least, you can also have a spiral line.
Dotted and dashed describe how a line is drawn, not its direction. A dotted or dashed line can also be vertical, horizontal or diagonal.
A line winds around a center point and gets farther from the center with each turn. What type of line is it?
Show answer
A spiral line. It is a curved line that keeps winding around its center.
Summary
- The two basic types of lines are straight lines and curved lines.
- A line has no endpoints, a ray has one endpoint, and a line segment has two endpoints.
- A vertical line goes straight up and down; a horizontal line is flat, with a slope of zero.
- A diagonal (oblique) line is neither vertical nor horizontal.
- Perpendicular lines meet at a right angle, like a horizontal line meeting a vertical line.
- Zigzag and staircase lines are made of straight lines that change direction.
- Wavy, spiral and closed curved lines are curved lines; a closed curved line ends where it begins.
- Dotted lines are made of dots and dashed lines are made of dashes.
Test Yourself: 10-Question Quiz
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