Collegedunia Team
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Line segments are defined as points along a line that are bounded by two distinct points. You can also think of a line segment as the portion of the line that connects two points. A line segment has two fixed or definite endpoints, but a line has no fixed endpoints and extends infinitely in both directions. A line segment is a part of a line that has two ends and is the shortest distance between them.
Table of Content
- Line Segment Definition
- Line segment Symbol
- Line Segment Measurement
- Line Segment Construction
- Line segment Examples
- Things to Remember
- Sample Questions
Also read: Isosceles Triangle Theorems
Line SegmentDefinition
There are always two endpoints in a line segment. Each segment of the line is always the same length since it is the distance between two fixed points. In this situation, you can measure the length in metric units such as centimeters (cm) or millimeters (mm), or use conventional units like feet or inches. As you study lines and angles,you will come across their basic terminologies. However, you will learn about their advanced versions.
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An open line segment is made up of only one of the two endpoints, whereas a closed segment has both of them. Line segments that have exactly one endpoint are called half-open segments.
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Line segmentSymbol
Line segments with two endpoints A and B are denoted with the bar symbol (—), such as AB.
Lines are typically illustrated by the left-right arrow (↔) and rays by arrows to the right(→).
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Line SegmentMeasurement
What is the best method for measuring a segment of a line? In this section, we will explore several methods.
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Observation-based
A simple observation is the most trivial way to compare two line segments. The length or shortness of two line segments can easily be determined by looking at them in comparison.
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As you can notice, by observation alone, line segment CD is longer than line segment AB in the above figure. However, this method is not without limitations since we cannot rely simply on observation whenever comparing two line segments.
Trace paper application
Trace paper makes it easy to compare line segments. By tracing one segment of a line and placing it over the other, it can be determined which is longer. Repeat the process as many times as necessary for multiple segments of a line.
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It is necessary to trace the line segments accurately to perform a precise comparison. As a result, this method relies on the accuracy of trace analysis, which limits its application.
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Line Segment Construction
The purpose of this lesson is to teach you how to draw a line segment with a compass and ruler. Consider a situation in which we need to draw a 5.6 cm long line segment. Here are the steps to follow:
- The length of the line segment should be considered when drawing any line without a measurement.
- Draw a line segment from point A to B, which will serve as the starting point.
- Use a ruler or scale to locate the compass’s pointer which is 5.6 cm from the pencil's lead.
- Place the pointer of your compass at point A on the line and mark an arc with your pencil using the same measurement.
- You can now mark this point as B
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Thus, AB is the 5.6 cm-long line segment that must be drawn.
Line SegmentExamples
Two-dimensional geometry has several examples of line segments as each polygon is made up of line segments.
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- The triangle is made up of three line segments connected end to end.
- There are four line segments that make up a square.
- Five-line segments make up a pentagon.
As a result, line segments play a crucial role in geometry
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Things to Remember
- There are always two endpoints in a line segment.
- It is the shortest distance between a line that has two endpoints.
- Line segments that have exactly one endpoint are called half-open segments.
- Line segments are denoted with the bar symbol (—).
- The triangle is made up of three line segments connected end to end.
- There are two ways to measure a line segment- Observation-based and Trace paper application.
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Sample Questions
Ques: Describe the concept of a line segment. What is the difference between a line segment and a line?
Answer: As the name suggests, a line segment is a portion of a line with two distinct endpoints. Those endpoints are definite.
In contrast to a line segment, which has endpoints, a line extends infinitely at both ends.
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Ques: Are there any differences between line segments and rays?
Answer:There is only one endpoint on a ray, while there are two on a line segment. In a ray, the endpoints are indeterminate, but in a line segment, the endpoints are always definite.
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Ques: How do you symbolize a line segment? What is an example of a line segment in real life?
Answer:A dotted line segment is denoted by a Bar (—) at the top of its notation, say AB.
There are many examples of line segments, including rulers, scales, sticks, boundary lines, etc.
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Ques: What are the Steps Involved in Constructing a Line Segment?
Answer:Assuming your task is to draw a line segment of 3 centimeters. Follow the below-mentioned steps to complete your task:
- Draw a straight line of no specific measurement keeping in mind that it is longer than the line segment you have to draw.
- Mark a dot C on the line which will be the starting point of your line segment.
- Now widen the compass and using a measuring scale, ensure that the distance between the tip of the compass and the tip of the pencil is 3 centimeters apart.
- Place the tip of the compass at point C on the line that you had drawn and draw an arc 3 centimeters from point C.
- Mark the point where the arc meets the line, as D.
- Hence, CD is the required line segment of length 3 centimeters.
Also Read:
CBSE X Related Questions
1.
The following table gives the distribution of the life time of 400 neon lamps :
Life time (in hours) Number of lamps 1500 - 2000
14
2000 - 2500
56
2500 - 3000
60
3000 - 3500
86
3500 - 4000
74
4000 - 4500
62
4500 - 5000
48
Find the median life time of a lamp.
1.
The following table gives the distribution of the life time of 400 neon lamps :
| Life time (in hours) | Number of lamps |
|---|---|
1500 - 2000 | 14 |
2000 - 2500 | 56 |
2500 - 3000 | 60 |
3000 - 3500 | 86 |
3500 - 4000 | 74 |
4000 - 4500 | 62 |
4500 - 5000 | 48 |
Find the median life time of a lamp.
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2.
If the median of the distribution given below is 28.5, find the values of x and y.
Class interval
Frequency
0 - 10
5
10 - 20
x
20 - 30
20
30 - 40
15
40 - 50
y
50 - 60
5
Total
60
2.
If the median of the distribution given below is 28.5, find the values of x and y.
Class interval | Frequency |
|---|---|
0 - 10 | 5 |
10 - 20 | x |
20 - 30 | 20 |
30 - 40 | 15 |
40 - 50 | y |
50 - 60 | 5 |
Total | 60 |
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3.
Draw the graphs of the equations\(x – y + 1 = 0 \)and\(3x + 2y – 12 = 0\). Determine the coordinates of the vertices of the triangle formed by these lines and the\(X\)-axis, and shade the triangular region.
3.
Draw the graphs of the equations\(x – y + 1 = 0 \)and\(3x + 2y – 12 = 0\). Determine the coordinates of the vertices of the triangle formed by these lines and the\(X\)-axis, and shade the triangular region.
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4.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
4.
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
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5.
If 3 cot A = 4, check whether\(\frac{(1-\text{tan}^2A)}{(1+\text{tan}^2A)}\)= cos2A – sin2A or not
5.
If 3 cot A = 4, check whether\(\frac{(1-\text{tan}^2A)}{(1+\text{tan}^2A)}\)= cos2A – sin2A or not
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6.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :
Lifetimes (in hours)
0 - 20
20 - 40
40 - 60
60 - 80
80 - 100
100 - 120
Frequency
10
35
52
61
28
29
Determine the modal lifetimes of the components.
6.
The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :
Lifetimes (in hours) | 0 - 20 | 20 - 40 | 40 - 60 | 60 - 80 | 80 - 100 | 100 - 120 |
|---|---|---|---|---|---|---|
Frequency | 10 | 35 | 52 | 61 | 28 | 29 |
Determine the modal lifetimes of the components.
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