What Are Segments in Geometry?

What are segments in geometry? Keep reading to learn all about what they are, the different types,  and how to calculate the distance of a line segment.

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In geometry, segments are portions of lines that are defined by two distinct endpoints. Segments are the smallest part of a circle when a line cuts across. If the segment is straight, it is called a line segment. If it is curved, it is called a curved segment.

Segments are elements of a circle geometry. The widely known elements are the radius, circumference, and diameter. You will understand more about segments as you read this article. 

What Is a Tangent Line in Calculus?

A tangent line is a straight line that touches a curve at that point. In calculus, a tangent line shares the same slope as the curve at the point where it touches it, representing how steep the curve is. 

The tangent line in calculus may touch or cross the curve at some other point on the curve. 

While a line segment is a part of a line bounded by two distinct endpoints, a tangent line is a straight line that touches a curve at a single point. The tangent line is peculiar to calculus, as the line segment is peculiar to geometry. 

How to Measure Line Segments?

A line segment can be measured using various methods, such as a ruler, measuring tape, a pair of dividers, and a scale or ruler. Let's explore each of these methods in detail:

Using a Ruler or Scale Only 

To measure the length of a line segment, we will begin by identifying the endpoints. The endpoints will determine the length of the line segment. Next, place the ruler on the line so that the 0 mark coincides with the endpoint A of the line segment. Then, read and record the measurement. 

Read the measurement by holding the scale properly along the line segment. Then, read the mark on the scale that coincides with point B on the line segment. Ensure that you note down the measurement obtained using the appropriate units based on the ruler's scale.

In the image above, we measure the line segment AB using a ruler with a centimeters ruler. The 0 mark on the ruler coincides with the starting point A, and the 7 cm mark coincides with the end point B. 

Thus, the length of this line segment AB is 7 cm.

Use a Pair of Dividers and a Scale or Ruler.

We can also use a pair of dividers to measure a line segment. We do that using a pair of dividers alongside a scale. A divider has two sharp pointed ends, which can be increased or decreased. 

A pair of dividers for measuring line segments. 

Source: Vectorstock

First, identify the endpoints of the line segments. Next, open the pair of dividers carefully and place the pointed ends on both endpoints of the line segment. Then, lift the pair of dividers carefully without altering its arms.

Now, pick a scale with suitable units. Place one end of the divider on the zero mark of the scale and the other end of the divider on the scale without disturbing its arms. Go ahead and measure the distance.

Practice Questions 

Find the length of lettered segments using the number lines given below:

1.

Source: Brilliant 

Answer: 5 cm

2.

Source: Study.com

Answer: AB-5 cm, CD-4 cm

3.

Source: Kristaking

Answer: 5cm

4.

Source: Study.com

Answer: AB-4cm, CD-4cm

5.

Source: Study.com

Answer: DE-5cm, FG-5cm

Types of Segments

There are different types of segments in geometry, including line segments, rays, collinear segments, coplanar segments, perpendicular bisectors, median segments, chords, and secant segments. Let's explore some of these segments. 

Line Segment

As mentioned earlier, a line segment is a straight line that connects two points. In geometry, the line runs from one point to another in a circle. 

Line segments usually have a definite length, which is the shortest distance between the two points. You can use line segments in geometry to measure distances, define polygon shapes, and determine intersections. In geometry, a line segment is represented by a bar on top of the alphabet, as in line AB. 

Ray

A ray is a line with a starting point extending infinitely in one direction. It is usually represented like this.

o-------------------------------------------------->

We utilize rays to represent half-lines, angles, and directions.

Perpendicular Bisector

A perpendicular bisector is another type of segment in geometry. It could be a line, ray, or segment intersecting another segment at a right angle and dividing it into two equal parts. 

It is called perpendicular because it forms a 90-degree angle with the other segment.

In geometry, perpendicular bisectors are used to construct perpendicular lines, determine right angles, and find the circumcenter of triangles.

Parallel Segments 

Parallel segments are the types of segment geometry that lie on the same plane and never intersect. They have the same slope and length. We use segment geometry to study parallel lines, transversals, and congruent angles in geometry.

Secant Segment

A secant segment is a line that intersects a circle at two distinct points. It is similar to the tangent line, but the tangent line touches the circle at one point. A secant segment creates a segment inside the circle and another outside it.

Secant connects two points on the circumference of the circle. In geometry, we use secant segments to study circle properties, chord lengths, and intersecting lines.

Difference Between Line, Line Segment, and Ray

Important Notes:

• While a line is indefinite, extending in both directions, a line segment is finite, with distinct endpoints defining its length.
• A ray is also indefinite, like a line, but has one endpoint and extends indefinitely in one direction.
• A line could be a beam of light without a source. Once the source is identified, it becomes a ray. 

Line Segment Problems: Example Exam Questions

There is a formula to calculate line segments in geometry. If we have the coordinates of the two endpoints, we can calculate the distance between the two points. The formula to calculate the length of the line segment is: 

D = √[(x₂−x₁)² + (y₂−y₁)²]. Here, (x₁,y₁) and (x₂, y₂) are the coordinates of the endpoints. 

For example, calculate the distance if a line segment has the following coordinates: (-1, 1) and (4, –3). Let us apply the distance formula to find the length of the line segment. Here, 

x₁ = -1; x₂ = 4; y₁ = 1; y₂ = -3. 

Substitute the values in the distance formula to have: 

D =√[(4-(-1))² + (-3-1)²) = √((4+1)² + (-3-1)²] = √(5)²+ (-4)²) = √(25 + 16) = √41 = 6.40 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (-1, 1) and (4, –3) is 6.40 units.

Practice Questions

Practice these questions and compare your answers to test your knowledge of line segments.

Question 1

A line segment is a:

1. One-dimensional figure
2. Two-dimensional figure
3. Three-dimensional figure
4. None of these

Answer: A. Line segments are one-dimensional figures. They have only length with no width.

Question 2

Which of these has two end-points?

1. Line segment
2. Ray segment

Answer: Line segment. A line segment has two endpoints.

Question 3

When the coordinates of the two endpoints are given, the length of a line segment can be calculated using the distance formula.

1. True
2. False

Answer: True. The length of a line segment can be determined if you have the coordinates of two endpoints.

Question 4

Identify if the given figure is a line segment, a line, or a ray.

M <--------------------------------------> N

Answer: MN is a line. The figure has two points with an arrow on both ends. This shows that it is not a line segment or a ray but a line.

Question 5

Find the length of the line segment PQ if the coordinates of P and Q are (2, 4) and (1, 0), respectively.

Answer: x₁ = 2; x₂ = 1; y₁ = 4; y₂ = 0. 

Substitute the values in the distance formula to have: 

D =√[(3-1)² + (0-4)²) = √(2)²+ (-4)²) = √(4 + 16) = √20 = 4.47 units. Therefore, using the distance formula, we found that the length of the line segment with coordinates (2, 4) and (1, 0) is 4.47 units

Question 6

How Many line segments does a Pentagon have?

1. Five
2. Six
3. Two
4. Three

Answer: A pentagon has 5 line segments

Question 7

Which of these is the unit of line segment?

1. Liters
2. Centimeter 
3. Kilogram
4. Cubic meter

Answer: Centimeter is a metric unit used to measure the line segment.

FAQs: What Are Segments in Geometry? 

If you have other questions about segments, we have answered them below. 

1. How Do You Apply Segments in Real Life?

In real life, we use segments to measure. Line segments, for example, measure distances between two points. They are used for items like the length of a road, the height of a building, or the width of a room. 

Architects and engineers also apply line segments to draw blueprints and designs for buildings, bridges, and other structures.

2. What Are Segments in a Triangle?

In a triangle, segments are the line segments formed by connecting the triangle's vertices, midpoints, and other points. Some common segments in a triangle include side segments, median segments, altitude segments, and angle bisector segments.

3. What Are Segments in a Polygon?

Segments in a polygon refer to the line segments formed by connecting the polygon's vertices. The different segments you can identify in a polygon include side, diagonal, perimeter, and interior segments. A rectangle is a polygon made of four line segments.

Final Thoughts

Line segments in geometry help us better understand elaborate shapes and structures. Typically defined by an initial point, an endpoint, and a direction, these segments offer insights into spatial relationships. Understanding their properties, such as length and midpoint, will provide solutions in different mathematical contexts. 

If you need help tackling line segments, or any other math concepts, feel free to reach out to one of our expert math tutors for personalized assistance. Whether you're grappling with basic concepts or diving into advanced theories, our tutors are equipped to guide you through every step of your mathematical journey!