An Overview of Practical Geometry Concepts
The chapter of Practical Geometry for Class 6 is meant to impart knowledge about the various geometrical quantities like angle, radius, length of the line segment, etc. The practical approach for calculating these quantities using multiple tools of construction is taught to you so that you can get acquainted with the intricacies of the chapter.
Now, learn the nuances of Practical Geometry Class 6 quickly and perform well in academics. You will be able to construct geometrical diagrams using the tools as you study from these notes and excel in academic ventures.
Practical Geometry – Learn with us
In order to start constructing geometrical figures, referring to NCERT solution for class 6 Maths Chapter 14 Practical Geometry is a necessity. Here, get familiar with the geometrical tools first.
Geometrical tools/ Instrument
Construction
A line segment
To construct a line segment of definite length, you need
Compass,
Ruler.
Step 1. Draw a line segment of any length using a ruler and mark a point ‘A’ anywhere.
Step 2. Take the compass and put the compass pointer on mark ‘0’ of scale. Stretch the pencil to a definite length; say at ‘5 cm’ on the ruler.
Step 3. Place the compass pointer at a point ‘A’ and draw a 5 cm arc intersecting the already drawn line segment. Mark the point of intersection as ‘B’. Now, ‘AB’ represents a line segment of length ‘5 cm’.
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Parallels and Perpendiculars
Using a ruler and compass –
Step 1. Draw a line ‘CB’ as shown in the picture below and mark a point ‘A’ as its centre. Put the compass pointer on ‘A’ and draw a big arc on it.
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Step 2. Keeping the compass length same as before, draw arcs by keeping points ‘C’ and ‘B’ as the centre so that they intersect at a point ‘D’.
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Step 3. Draw a perpendicular from point ‘D’ to ‘A’.
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Circle
You can easily construct a circle of the known radius using a compass. Put the compass pointer at ‘0’ in ruler and draw the pencil for a specific radius. Keeping ‘O’ as the centre place the compass pointer on it and rotate the compass to make a full circle.
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Angles
In Class 6 Maths Practical Geometry, you will find numerous questions that ask you to determine angles or draw angles. You can either use a protractor or a compass. The use of protractor is easy as you need to place the point ‘0’ at the vertex alongside one line and measure the angle made by another line on it, by marking it on the protractor.
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Draw 600 angle –
Step 1. Draw a straight line segment m and mark a point ‘C’ on it.
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Step 2. Put the compass pointer on point ‘C’ and draw an arc on the line and name it ‘D’. Now, taking the point ‘D’ as centre draw another arc so that it intersects the previous arc and name it as ‘E’.
Step 3. Draw a straight line from C to E to make an angle of 600 with line m.
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Draw 1200 angle –
Step 1. Draw a straight line segment m and mark a point ‘C’ on it.
Step 2. Put the compass pointer on point ‘C’ and draw a big arc on the line and name it ‘D’. Now, taking the point ‘D’ as centre draw another arc so that it intersects the previous arc and name it as ‘E’.
Step 3. Place the compass pointer on ‘E’ and make another arc on the ‘D’ arc and name it as ‘F’. Join the points ‘C’ and ‘F’ to make an angle of 1200.
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Now that you are familiar with the concepts of NCERT Class 6 Maths Practical Geometry, you will be able to practice questions and exercises quickly.
In case you want to increase your understanding of the subject, you can refer to Vedantu’s Practical Geometry Class 8 solutions. Refer to our Practical Geometry Class 7 notes and improve your academic performance. Download Vedantu’s app now and excel in academics.
FAQs on Practical Geometry
1. How do the NCERT Solutions for Class 6 Maths Chapter on Practical Geometry help with homework and exams?
The NCERT Solutions for Class 6 Maths Practical Geometry provide step-by-step guidance for every problem in the textbook. They are prepared according to the CBSE 2025-26 syllabus, ensuring you learn the correct methods for constructing geometric shapes. By following these solutions, you can understand the logic behind each construction, practice for exams, and accurately complete your homework assignments.
2. What are the essential instruments needed to solve problems in the NCERT Class 6 Practical Geometry chapter?
To correctly solve the problems in Class 6 Practical Geometry, you will need the following instruments from a geometry box:
- A graduated ruler for measuring and drawing line segments.
- A pair of compasses for drawing arcs and circles of a specific radius.
- A divider to compare lengths.
- A protractor to measure and draw angles.
- A pair of set-squares for drawing parallel and perpendicular lines.
- A well-sharpened pencil for precision.
3. What is the step-by-step method to construct a perpendicular to a line from a point on the line itself?
To construct a perpendicular to a line 'l' from a point 'P' on it, follow these NCERT-prescribed steps:
- Step 1: Place the compass point on P and draw an arc that cuts the line 'l' at two points, A and B.
- Step 2: Now, place the compass point on A and, taking a radius greater than AP, draw an arc above the line.
- Step 3: Without changing the compass radius, place the compass point on B and draw another arc that intersects the first arc at a point, Q.
- Step 4: Join the points P and Q. The line PQ is the required perpendicular to line 'l'.
4. How do you construct a 90° angle using only a ruler and compass as per the NCERT method?
Constructing a 90° angle involves creating a perpendicular on a line. Here are the steps:
- Step 1: Draw a line and mark a point P on it.
- Step 2: With P as the centre, draw an arc that intersects the line at two points, A and B.
- Step 3: With A as the centre and a radius more than half of AB, draw an arc.
- Step 4: With B as the centre and the same radius, draw another arc to intersect the previous one at point Q.
- Step 5: Join P and Q. The angle ∠QPA is the required 90° angle. This method constructs a perpendicular, which is by definition at 90 degrees to the line.
5. What is the real difference between 'drawing' a shape and 'constructing' a shape in Practical Geometry?
'Drawing' a shape implies creating a sketch or a representation that might not be perfectly accurate. For instance, you might use a protractor to 'draw' a 60° angle. However, 'constructing' a shape is a precise process that uses only a ruler and a compass. It relies on pure geometric principles, like using arcs to find exact points, ensuring the final figure is geometrically perfect and not just an approximation.
6. What are the most common mistakes students make while constructing the perpendicular bisector of a line segment?
When constructing a perpendicular bisector, students should avoid these common errors:
- Incorrect Radius: Taking a compass radius that is less than or equal to half the length of the line segment. The arcs will not intersect if the radius is too small.
- Changing Compass Width: Altering the compass radius after drawing the first arc. The radius must remain the same for the arcs drawn from both endpoints.
- Sloppy Arcs: Drawing thick or imprecise arcs, which makes it difficult to identify the exact intersection point. Use a sharp pencil for clean lines.
7. Why is a compass and ruler considered more fundamental in geometric constructions than a protractor?
A compass and a ruler are considered fundamental because they are based on the foundational axioms of Euclidean geometry—creating circles of a set radius and drawing straight lines. Constructions made with these tools are derived from logical geometric proofs. A protractor, on the other hand, is a measuring tool. Using it is like measuring an answer rather than deriving it from first principles. Therefore, true geometric 'construction' relies on the logical purity of the compass and ruler method.
8. After constructing the bisector of an angle, how can you check if your solution is correct without using a protractor?
You can verify the accuracy of your angle bisector using a simple paper folding technique. Trace the angle and its bisector onto a piece of paper. Carefully fold the paper along the constructed bisector line. If the two arms of the original angle perfectly overlap each other, your construction is accurate. This method physically demonstrates that the bisector has divided the angle into two equal halves.
9. How are the basic construction skills from Class 6 Practical Geometry used in real life?
The skills learned in Practical Geometry are the foundation for many professional fields. For example:
- Architecture and Engineering: Architects use principles of perpendicular lines, parallel lines, and specific angles to design stable and functional blueprints for buildings.
- Design: Graphic designers and artists use geometric constructions to create symmetrical logos, patterns, and art.
- Carpentry: Carpenters construct perpendicular bisectors to find the centre of wooden beams or to ensure corners are perfectly square (90 degrees).
