Geometrical Instruments – Description and Uses

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We come across a number of shapes in our day-to-day life. You are already aware of a couple of them such as triangles, squares, hexagons, circles, parallelograms, and so on. The branch of Maths that studies these shapes is called Geometry. In Maths, practical geometry is the most crucial topic, where we learn about the shapes of objects and how to draw them.

Be it the Eiffel Tower in Paris or the beautiful Taj Mahal in India, all these astounding monuments are a miracle of geometry. Not only man-made works but the beauty of geometry could be found in mother nature herself! 

Let’s understand what are geometrical instruments or geometrical tools and their uses.

What are Geometrical Instruments?

In geometry, we draw different types of shapes to solve problems. Geometrical instruments are instruments used to draw different types of geometric shapes.  There are different types of geometric tools to draw these shapes. Different figures have characteristic properties such as length, breadth, diameter, etc. which set them apart from one another and are parameters to produce the figures on paper. Practical geometry or Euclidean geometry is the most pragmatic branch of geometry that deals with the construction of different geometrical figures using geometric instruments such as rulers, compasses, and protractors.

The early geometers studied figures such as points, lines, and angles which required the use of rulers and compasses only. With the advent of more geometric designs, other geometric tools were invented. Some of the most commonly used geometric tools are:

  • Ruler
  • Compass
  • Protractor
  • Divider
  • Set-squares

Now, let us discuss the different Maths tools with their description and uses in detail.

Ruler – Geometry Tool to Draw Lines

A ruler is also called a straightedge. The name straightedge was more commonly used in the early days. Nowadays people use the word ruler. Now, a straightedge does what its name implies, that is, to draw straight edges. Thus, a ruler is used whenever we need to draw simple straight lines. The required length of the line is measured and then drawn. Now the measurement of the line can be in any form of the measurement unit. 

geometrical instruments

The most commonly used measurement scales are the centimeter scale, the meter scale, and the inches scale. Often the centimeter scale consists of a millimeter scale on one side and then the inches scale on the other side of the ruler.

Compass – Geometry Drawing Tool to Draw Circles

It is a ‘V-shaped tool that holds a pencil on one side of the ‘V’ and a pointer on the other side. The distance between the pencil and the pointer is adjustable. It is used to trace arcs, circles, and angles. It is also used to mark equal lengths. A compass is one of the mathematical tools which is used to draw a geometrical figure, such as a circle. It is also used in the intersection of line segments and tools, which is used to intersect the line segment and helps to find the midpoint of the shapes.

geometrical instruments

Protractor – Geometry Tool to Measure Angles

When we need to draw some angle then we use the geometrical tool known as a protractor. The protractor scale is graduated in degrees. Thus, it can also be used to measure any unknown angle. Generally, a protractor consists of a graduation scale from 0 degrees to 180 degrees. But it can also consist of a whole 360 degrees of graduations, that is, a full circle.

geometrical instruments

Divider – Geometry Drawing Tool to Compare Lengths

It looks similar to the compasses with its V-shaped structure. However, it has pointers on both ends of the ‘V’. The distance between them is adjustable and it is used to measure and compare lengths.

geometrical instruments

The terms divider and compass are often used to mark the distance or mark divisions. The major difference between the compass and divider is that the compass is defined as a drafting instrument, in which one sharp point is positioned at centre and the other point has a pen or pencil to describe the circle or other functionality. Whereas the divider has two sharp points, in which one sharp point is used as a centre, and the other sharp point is used for marking.

Set-Squares – Geometry Tool to Draw Parallel and Perpendicular Lines

Now, if we need to draw a parallel line or even a perpendicular line then we can use a set square. To talk about the structure of a set square has a body that is usually made up of plastic. It is triangular and consists of graduations that can vary. There are usually two types of set squares. 

  • One is where the three angles of the triangle are 90 degrees and 45 and 45 degrees
  • The other has angles of 90, 60, and 30 degrees
geometrical instruments
Famous Mathematicians

Advantages of Geometry Tools

With the help of tools, we can enhance our ability to do certain things and help us in accomplishing certain projects which would be otherwise, nearly impossible to achieve. To do a job we may need more than a single type of tool. In fact, more than often it is possible that that might require more than one type of tool. In order to draw the various types of geometrical shapes, we require various tools. To draw the shapes of practical geometry we require tools like a ruler, a compass, a protractor, set squares, roller scales, and a divider, known as geometrical tools. 

In the early days, the mathematicians who used to study the various geometrical shapes and sizes used simple geometrical tools like a ruler and a compass. With more and more knowledge and the increasing need for new structural designs, a greater number of geometrical tools were incorporated in the field of geometry.

Practice Problems

  1. What are geometrical instruments?
  2. What are the two most important geometrical tools used in geometric constructions?
  3. What is the use of a ruler?
  4. What is the use of a compass?
  5. What is the use of a protractor?
  6. What is the use of set squares?
  7. What is the use of a divider?


What are Geometric Tools in Maths?

Geometric tools are those instruments that are used to construct different types of geometric shapes and figures. In Euclidean geometry, all the shapes, lines, and angles are drawn using geometric tools.

What are the 2 most important Euclidean tools used in Geometric construction?

The two most important Euclidean tools used by early Greeks to construct different geometrical shapes and angles were a compass and a straightedge. Using these two tools, almost any shape can be constructed. Later, rulers and protectors were invented which made construction easier.

What are the most common instruments in a geometry box?

The most common tools in a student geometric box are:
a. Compass
b. Ruler
c. Protractor
d. Divider
e. Set-squares

What is the use of a ruler in Geometry?

In Geometry, a ruler is used to draw straight lines. Rulers are also used to measure the length of the object.

Why do we use protractors in Maths?

A protractor is used to measure the angles. The protractor is graduated from 0 degrees to 180 degrees, which helps to measure the angle value. It has two sets of markings from 0-180 degrees from left to right as well as from right to left. The inner and outer angles will add up to 180 degrees.


Geometry is a branch of Mathematics that studies shapes. In practical geometry, we draw different types of geometric shapes. The tools or instruments that are used to draw these shapes are called geometrical instruments or geometrical tools. The commonly used geometrical instruments are rulers, compasses, protractors, set squares, and dividers.

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