Step by Step Practical Geometry Constructions with Solved Examples and Key Properties
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’.
Image will be uploaded soon
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.
Image will be uploaded soon
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’.
Image will be uploaded soon
Step 3. Draw a perpendicular from point ‘D’ to ‘A’.
Image will be uploaded soon
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.
Image will be uploaded soon
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.
Image will be uploaded soon
Draw 600 angle –
Step 1. Draw a straight line segment m and mark a point ‘C’ on it.
Image will be uploaded soon
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.
Image will be uploaded soon
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.
Image will be uploaded soon
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 Concepts and Construction Methods
1. What is practical geometry in Maths?
Practical geometry is the branch of mathematics that deals with constructing geometric shapes and figures using tools like a compass, ruler, and protractor. It focuses on accurate geometric constructions such as drawing angles, triangles, circles, and perpendicular bisectors. Unlike theoretical geometry, practical geometry emphasizes step-by-step construction methods used in classrooms, engineering drawing, and design.
2. What instruments are used in practical geometry?
The main instruments used in practical geometry are a compass, ruler (scale), protractor, and set squares. These tools help in accurate geometric constructions:
- Compass: Draws circles and arcs
- Ruler: Draws straight lines and measures length
- Protractor: Measures and constructs angles
- Set squares: Draw perpendicular and parallel lines
3. How do you construct a perpendicular bisector of a line segment?
To construct a perpendicular bisector, draw arcs from both endpoints of the line segment with equal radius greater than half its length and join their intersection points. Steps:
- Draw line segment AB.
- With A as center, draw arcs above and below AB.
- With B as center and same radius, draw arcs cutting the previous arcs.
- Join the intersection points of arcs.
4. How do you construct an angle of 60° using a compass?
An angle of 60° is constructed by forming an equilateral triangle using equal arcs. Steps:
- Draw a line segment AB.
- With A as center, draw an arc.
- With B as center and same radius, cut the arc at point C.
- Join AC.
5. How do you construct a triangle when three sides are given?
A triangle can be constructed using the SSS (Side-Side-Side) method when all three sides are given. Steps:
- Draw base AB equal to one given side.
- With A as center, draw an arc equal to the second side.
- With B as center, draw an arc equal to the third side.
- Mark intersection point C and join AC and BC.
6. What is the difference between a locus and a construction in practical geometry?
A locus is the path traced by a moving point satisfying a condition, while a construction is the method of drawing a geometric figure using tools. For example:
- The locus of points equidistant from two points is the perpendicular bisector.
- Constructing a perpendicular bisector involves drawing arcs and joining points.
7. How do you construct parallel lines using a ruler and compass?
Parallel lines can be constructed by copying corresponding angles using a compass. Steps:
- Draw given line l and mark a point P outside it.
- Draw a transversal through P intersecting l.
- Copy the angle formed at the intersection using arcs.
- Draw a line through P making the copied angle.
8. How do you construct the circumcenter of a triangle?
The circumcenter is found by drawing the perpendicular bisectors of at least two sides of a triangle. Steps:
- Construct perpendicular bisector of side AB.
- Construct perpendicular bisector of side BC.
- Mark their intersection point O.
9. How do you construct the incircle of a triangle?
The incircle is constructed by locating the incenter using angle bisectors. Steps:
- Draw angle bisector of angle A.
- Draw angle bisector of angle B.
- Their intersection point I is the incenter.
- Draw a perpendicular from I to any side to get radius.
- With I as center, draw the circle.
10. Why is practical geometry important in real life?
Practical geometry is important because it develops accurate drawing and spatial reasoning skills used in engineering, architecture, and design. It helps in:
- Creating technical drawings and blueprints
- Designing buildings and structures
- Solving real-world measurement problems
- Understanding geometric properties visually
