Chapter 14
PRACTICAL GEOMETRY
Practical geometry is an important branch of geometry which deals with the study of the size, positions, shapes as well as dimensions of objects.
Geometrical Instruments
Whether you have to draw a line segment or measure it, draw a circle or arcs, draw an angle, etc. it can easily be possible with the help of geometrical tools. Let us discuss the various geometrical instruments used in practical geometry.
![Practical Geometry](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_1-7.png)
Points and Lines
Point: It is a location.
Line: Collection of points in a linear manner that extends infinitely in two directions.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_2-7.png)
Tools of Construction
Tools used for construction:
Ruler: An instrument used to draw line segments and measure their lengths.
Compass: Instrument having a pointer on one end and a pencil on the other end. It is used to mark equal lengths and to draw circles and arcs.
Divider: Instrument having a pair of pointers. It is used to compare lengths.
Set- Squares: Two triangular pieces – One of them has 45°, 45°, 90° and the other has 30°, 60°, 90° angles at the vertices. It is used to draw parallel and perpendicular lines.
Protractor: A semicircular instrument graduated into 180° parts. It is used to draw and measure angles.
![Practical Geometry](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_3-7.png)
Line Segment
Line Segment: Part of a line that is bounded by two distinct endpoints.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_4-7.png)
Constructing a Line Segment for a given Length
Steps for constructing a line segment of a given length ‘a’:
(i) Draw a line l and mark a point A on it.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_5-6.png)
Also Read :-Mathematics chapter 11 Algebra
(ii) Place the compass on the initial point of the ruler. Open it to place pencil point up to the ‘a’ mark.
(iii) Place the pointer on A and draw an arc to cut l at B. AB is the required line segment.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_6-5.png)
Constructing Copy of a Line Segment
Steps for constructing a copy of a given line segment using ruler and compass together:
(i) Given AB whose length is unknown.
(ii) Fix compass’ pointer on A and pencil end on B. The opening of the instrument now gives the length of AB.
(iii) Draw any line l.
(iv) Placing the pointer on C, draw an arc that cuts l at a point say D. Then, CD = AB.
To know more about Constructing a Copy of a Line Segment, visit here.
Perpendiculars and Parallels
A line MN meeting another line AB at the right angle is said to be the perpendicular to the line AB.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_7-5.png)
If two lines are non-intersecting and are always the same distance apart, then they are said to be parallel lines.
As shown in the figure, AB || CD.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_8-5.png)
Constructing a Perpendiculars Using a Compass and Ruler
Steps for constructing perpendiculars using compass and rulers:
(i) Given a line I and a point P not on it.
(ii) With P as the centre, draw an arc which intersects line I at two points A and B.
(iii) Using the same radius and with A and B as centres, construct two arcs that intersect at a point, say Q, on the other side.
(iv) Join PQ. Thus, PQ is the perpendicular to l.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_9-5.png)
Constructing Perpendicular to a Line through a Point on the Line
Steps to construct a perpendicular to a line through a point on the line:
(i) Place a ruler along a given line l such that one of its edges is along l.
(ii) Place a set square with one of its edges along the already aligned edge of the ruler.
(iii) Slide the set square such that its right-angled corner coincides with the Point P.
(iv) Draw PQ and PQ are perpendicular to l.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_10-5.png)
Also Read :-Mathematics chapter 9 Data Handling
Paper Folding Construction
Paper folding method to make perpendiculars:
(i) Let l be the given line and P be a point outside l.
(ii) Place a set-square on l such that one arm of its right angle aligns along l.
(iii) Place a ruler along the edge opposite to the right angle of the set-square.
(iv) Slide the set-square along the ruler till the point P touches the other arm of the set-square.
![Practical Geometry](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_11-4.png)
Circle
A circle is a set of all points in a plane that are equidistant from a point i.e. centre of the circle.
To know more about Circles,
Construction of a Circle for a given Radius
Steps for constructing a circle using a compass:
(i) Open compass for the required radius.
(ii) Place pointer of the compass on O.
(iii) Rotate the compass slowly to draw the circle.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_12-4.png)
Angle Bisector and Its Construction
Steps to construct angle bisectors of a given angle:
(i) With O as the centre, draw an arc that cuts both rays at A and B.
(ii) With B as the centre, draw an arc whose radius is more than half of the length of AB.
(iii) With A as the centre, with the same radius, cut an arc in the interior of ∠BOA
(iv) Mark point of intersection as C. Then, OC is the angle bisector.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_13-3.png)
Construction of 30°, 60°, 90°and 120°Angles
(i) Construction of 60° angle:
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_14-3.png)
(ii) Construction of 120°angle:
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_15-3.png)
(iii) Construction of 90° angle:
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_16-3.png)
(iv) Construction of 30° angle:
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_17-3.png)
Constructing of an Angle with Unknown Measurement
Steps for constructing a copy of an angle with unknown measurement:
(i) Draw a line l and choose a point P on it.
(ii) Place compass’ pointer at A and draw an arc to cut the rays of ∠A at B and C.
(iii) Draw an arc with P as the centre, cutting /at Q.
(iv) Set your compasses to length BC with the same radius.
(v) Place the compasses pointer at Q and draw an arc to cut the arc drawn earlier in R.
(vi) Join PR. This gives ∠P=∠A
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_18-2.png)
Angles
Angles: Formed by two rays sharing a common endpoint.
![](https://gyanchakra.co.in/wp-content/uploads/2023/03/Screenshot_19-2.png)
Also Read :-Mathematics chapter 13 Symmetry
![Practical Geometry](https://gyanchakra.co.in/wp-content/uploads/2023/03/unnamed-13-1024x749.jpg)
NCERT Notes
Nursery Class | Ncert Notes for Class 1 | Ncert Notes For Class 2 | Ncert Notes For Class 3 | Ncert Notes For Class 4 | Ncert Notes for class 5 | Ncert Notes for Class 6 | Ncert Notes For Class 7 | Ncert Notes for Class 8 | Ncert Notes for Class 9 | Ncert Notes for class 10 | Ncert Notes for class 11 Science | Ncert Notes for class 11 Commerce | Ncert Notes for Class 11 Arts | Ncert Notes for class 12 Science | Ncert Notes for class 12 Commerce | Ncert Notes for class 12 Arts
Exams
UPSC Exam | SSC CGL Exam | SBI PO Exam | IBPS PO Exam | RRB NTPC Exam | RBI Exam | JEE Main Exam | NEET Exam | Gate Exam | CLAT Exam | RPSC RAS Exam
Shop at Gyanchakra
E- books | Nursery Books | Class 1 to 12 | Entrance Exams | Govt Exams | Skills | Courses | Games & Toys | Motivational Items
Follows on Social Media
Facebook | Youtube | Instagram | Pinterest | Medium | Linkedin |
Important Govt Sites
CBSE | NCERT | JEE | UPSC | NEET | SSC | PMO | Raj Board | RAS Exam |
Blogs
Current Affairs | Geography | Grammar | UPSC Exam | Higher Education | CBSE | Science Facts For Kids | JEE Exams | JEE Advance Exams | JEE mains Exams | NEET Exams | Science Facts For Students
Free Test Series for Entrance exams
Free Test Series for WBJEE | Free Test series for UPSEE | Free Test Series for AP EAMCET | JEE Mains Advanced | Free Test Series for BITSAT | Free Test Series for TS EAMCET | Free Test Series for Manipal Entrance Test MET | Free Test Series for CIPET JEE | Free Test Series for AIEEA UG Exam ICAR | Free Test Series for IISER SCB | Free test series for NEST National Entrance Screening Test | Maths Question Bank | Free Test Series for MHT CET | Free Test Series for GOA CET | Free Test For SRMJEEE
Healthy Nutrition for students
Healthy Snacks | Low Glycemic index Food | High Protien Food | Heart healthy | Low Calorie Foods | Dairy Free Foods | Gluten Free Foods | Keto Friendly Foods | Gut Healthy
Free Test Series for Govt Exams
Free Test Series for UPSC Prelims | Free test series for UPSC Drug Inspector | Free Test Series for TNPSC | Free Test Series for MPSC | Free Test Series for MPPSC | Free test Series for CGPSC | Free test Series for UPPSC | Free test Series for RPSC | Free Test series for Meghalaya PSC | Free Test Series for JPSC | Free Test Series for KPSC | Free Test Series for UKPSC | Free Test Series for OPSC |
Free Notes for NCERT Class 1
Free Video Notes for NCERT Class 1 EVS | Free Notes for NCERT Class 1 Mathematics | Free Video Notes for NCERT Class 1 Mathematics | Free Notes for NCERT Class 1 English | Free Video Notes for NCERT Class 1 Hindi | Free Video Notes for NCERT विज्ञान | Free Video Notes For NCERT गणित
Free Notes For NCERT Class 2 English medium
Free Video Notes for NCERT Class 2 EVS | Free video Notes for NCERT Class 2 Mathematics | Free Notes for NCERT Class 2 Mathematics | Free Notes for NCERT Class 2 English
Free Notes for NCERT Class 2 Hindi Medium
Free Notes for NCERT Class 2 Hindi | Free video Notes for Ncert Class 2 विज्ञान | Free Video Notes for NCERT Class 2 गणित |
Free Notes for NCERT class 3 English Medium
Free Video Notes for Ncert Class 3 EVS | Free Notes for Ncert class 3 EVS | Free Video Notes For Ncert Class 3 Mathematics | Free Notes for Ncert Class 3 Mathematics | Free Notes for Ncert Class 3 english | Free video Notes for Ncert Class 3 hindi | Free Video Notes for Ncert Class 3 विज्ञान
Free Notes for NCERT class 3 Hindi Medium
Free Video Notes for NCERT class 3 EVS Hindi Medium
Free Notes for NCERT class 4 English Medium
Free Video Notes for Ncert Class 4 EVS | Free Notes for Ncert class 4 EVS | Free Video Notes For Ncert Class 4 Mathematics | Free Notes for Ncert Class 4 Mathematics | Free Notes for Ncert Class 4 english | Free video Notes for Ncert Class 4 hindi
Free Notes for NCERT class 4 Hindi Medium
Free Video Notes for NCERT class 4 EVS Hindi Medium | Free Video Notes for NCERT class 4 Maths Hindi Medium
Free Notes for NCERT class 5 English Medium
Free Video Notes for Ncert Class 5 EVS | Free Notes for Ncert class 5 EVS | Free Video Notes For Ncert Class 5 Mathematics | Free Notes for Ncert Class 5 Mathematics | Free Notes for Ncert Class 5 english | Free video Notes for Ncert Class 5 hindi
Free Notes for NCERT class 5 Hindi Medium
Free Video Notes for NCERT class 5 EVS Hindi Medium | Free Video Notes for NCERT class 5 Maths Hindi Medium
Free Notes for NCERT class 6 English Medium
Free Video Notes for Ncert Class 6 Science | Free MCQ for NCERT Class 6 Science | Free Notes for Ncert class 6 Science | Free Video Notes For Ncert Class 6 Mathematics | Free MCQ for NCERT Class 6 Mathematics | Free Notes for Ncert Class 6 Mathematics | Free Notes for Ncert Class 6 english | Free Video Notes for Ncert Class 6 Social Science | Free MCQ for NCERT Class 6 Social Science | Free Notes for Ncert class 6 Social Science
Free Notes for NCERT class 6 Hindi Medium
Free Video Notes for NCERT class 6 Science Hindi Medium | Free Notes for NCERT class 6 Science Hindi Medium | Free Video Notes for NCERT class 6 Mathematics Hindi Medium | Free Notes for NCERT class 6 Mathematics Hindi Medium | Free Notes for NCERT class 6 English Hindi Medium | Free Notes for NCERT class 6 Social Science Hindi Medium | Free Notes for NCERT class 6 Hindi in Hindi Medium
Free Notes for NCERT class 7 English Medium
Free Video Notes for Ncert Class 7 Science | Free MCQ for NCERT Class 7 Science | Free Notes for Ncert class 7 Science | Free Video Notes For Ncert Class 7 Mathematics | Free MCQ for NCERT Class 7 Mathematics | Free Notes for Ncert Class 7 Mathematics | Free Notes for Ncert Class 7 english | Free Video Notes for Ncert Class 7 Social Science | Free MCQ for NCERT Class 7 Social Science | Free Notes for Ncert class 7 Social Science | Free Notes for Ncert class 7 English
Free Notes for NCERT class 7 Hindi Medium
Free Video Notes for NCERT class 7 Science Hindi Medium | Free Notes for NCERT class 7 Science Hindi Medium | Free Video Notes for NCERT class 7 Mathematics Hindi Medium | Free Notes for NCERT class 7 Mathematics Hindi Medium | Free Notes for NCERT class 7 English Hindi Medium | Free Notes for NCERT class 7 Social Science Hindi Medium | Free Notes for NCERT class 7 Hindi in Hindi Medium
Free Notes for NCERT class 8 English Medium
Free Video Notes for Ncert Class 8 Science | Free MCQ for NCERT Class 8 Science | Free Notes for Ncert class 8 Science | Free Video Notes For Ncert Class 8 Mathematics | Free MCQ for NCERT Class 8 Mathematics | Free Notes for Ncert Class 8 Mathematics | Free Notes for Ncert Class 8 english grammar | Free Video Notes for Ncert Class 8 Social Science | Free MCQ for NCERT Class 8 Social Science | Free Notes for Ncert class 8 Social Science | Free Notes for Ncert class 8 English
Free Notes for NCERT class 8 Hindi Medium
Free Video Notes for NCERT class 8 Science Hindi Medium | Free Notes for NCERT class 8 Science Hindi Medium | Free Video Notes for NCERT class 8 Mathematics Hindi Medium | Free Notes for NCERT class 8 Mathematics Hindi Medium | Free Notes for NCERT class 8 English Hindi Medium | Free Notes for NCERT class 8 Social Science Hindi Medium | Free Notes for NCERT class 8 Hindi in Hindi Medium
Free Notes for NCERT class 9 English Medium
Free Video Notes for Ncert Class 9 Science | Free MCQ for NCERT Class 9 Science | Free Notes for Ncert class 9 Science | Free Video Notes For Ncert Class 9 Mathematics | Free MCQ for NCERT Class 9 Mathematics | Free Notes for Ncert Class 9 Mathematics | Free Notes for Ncert Class 9 english | Free Video Notes for Ncert Class 9 Social Science | Free MCQ for NCERT Class 9 Social Science | Free Notes for Ncert class 9 Social Science
Free Notes for NCERT class 9 Hindi Medium
Free Video Notes for NCERT class 9 Science Hindi Medium | Free Notes for NCERT class 9 Science Hindi Medium | Free Video Notes for NCERT class 9 Mathematics Hindi Medium | Free Notes for NCERT class 9 Mathematics Hindi Medium | Free Notes for NCERT class 9 English Hindi Medium | Free Notes for NCERT class 9 Social Science Hindi Medium | Free Notes for NCERT class 9 Hindi in Hindi Medium
Free Notes for NCERT class 10 English Medium
Free MCQ for NCERT Class 10 Science | Free Notes for Ncert class 10 Science | Free MCQ for NCERT Class 10 Mathematics | Free Notes for Ncert Class 10 Mathematics | Free Notes for Ncert Class 10 english | Free MCQ for NCERT Class 10 Social Science
Free Notes for NCERT class 10 Hindi Medium
Free Notes for NCERT class 10 Science Hindi Medium | Free Notes for NCERT class 10 Mathematics Hindi Medium | Free Notes for NCERT class 10 English Hindi Medium | Free Notes for NCERT class 10 Social Science Hindi Medium | Free Notes for NCERT class 10 Hindi in Hindi Medium
Free Notes for NCERT class 11 PCMB English Medium
Free Notes for Ncert class 11 Science | Free MCQ for NCERT Class 11 Science | Free Video Notes for Ncert class 11 Science | Free Notes for Ncert Class 11 Mathematics | Free MCQ for NCERT Class 11 Mathematics | Free Video Notes for Ncert Class 11 Mathematics | Free Notes for Ncert Class 11 english | Free Notes for NCERT Class 11 Physical Education
Free Notes for NCERT class 11 PCMB Hindi Medium
Free Notes for Ncert class 11 Science Hindi Medium | Free Video Notes for Ncert class 11 Science Hindi Medium | Free Notes for Ncert Class 11 Mathematics Hindi Medium | Free Video Notes for Ncert Class 11 Mathematics Hindi Medium | Free Notes for Ncert Class 11 english | Free Notes for NCERT Class 11 Physical Education Hindi Medium | Free Notes for Ncert Class 11 Hindi
Free Notes for NCERT class 11 Art Hindi Medium
Free Notes for Ncert class 11 Art अर्थशास्त्र सांख्यिकी Hindi Medium | Free Notes for Ncert class 11 Art इतिहास Hindi Medium | Free Notes for Ncert Class 11 Art समाजशास्त्र Hindi Medium | Free Notes for Ncert Class 11 Art भूगोल Hindi Medium | Free Notes for NCERT Class 11 Art राजनीति विज्ञान Hindi Medium | Free Notes for NCERT Class 11 Art हिन्दी Hindi Medium | Free Notes for NCERT Class 11 Art अंग्रेज़ी Hindi Medium | Free Notes for NCERT Class 11 Art शारीरिक शिक्षा Hindi Medium
Free Notes for NCERT class 11 Commerce English Medium
Free Notes for Ncert class 11 Commerce Physical Education | Free Notes for NCERT Class 11 Commerce English | Free Notes for Ncert class 11 Commerce Accountancy | Free MCQ for Ncert Class 11 Commerce Accountancy | Free Notes for NCERT Class 11 Commerce Entrepreneurship | Free Notes for Ncert Class 11 Commerce Economics Micro-Economics | Free MCQ for Ncert Class 11 Commerce Economics Micro-Economics | Free Notes for NCERT Class 11 Commerce Economics Statistics | Free MCQ for NCERT Class 11 Commerce Economics Statistics | Free Notes for NCERT Class 11 Commerce Business Studies | Free MCQ for NCERT Class 11 Commerce Business Studies
Free Notes for NCERT class 11 Commerce Hindi Medium
Free Notes for Ncert class 11 Commerce शारीरिक शिक्षा | Free Notes for NCERT Class 11 Commerce व्यवसाय अध्ययन | Free Notes for Ncert class 11 Commerce अंग्रेज़ी | Free Notes for NCERT Class 11 Commerce हिंदी | Free Notes for Ncert Class 11 Commerce अर्थशास्त्र सांख्यिकी | Free Notes for NCERT Class 11 Commerce अर्थशास्त्र व्यष्टि अर्थशास्त्र | Free Notes for NCERT Class 11 Commerce लेखाशास्त्र | Free Notes for NCERT Class 11 Commerce गणित
Free Notes for NCERT class 12 PCMB English Medium
Free Notes for Ncert class 12 Science | Free MCQ for NCERT Class 12 Science | Free Video Notes for Ncert class 12 Science | Free Notes for Ncert Class 12 Mathematics | Free MCQ for NCERT Class 12 Mathematics | Free Video Notes for Ncert Class 12 Mathematics | Free Notes for Ncert Class 12 english | Free Notes for NCERT Class 12 Physical Education
Free Notes for NCERT class 12 PCMB Hindi Medium
Free Notes for Ncert class 12 Science Hindi Medium | Free Video Notes for Ncert class 12 Science Hindi Medium | Free Notes for Ncert Class 12 Mathematics Hindi Medium | Free Video Notes for Ncert Class 12 Mathematics Hindi Medium | Free Notes for Ncert Class 12 english | Free Notes for Ncert Class 12 Hindi
Free Notes for NCERT class 12 Art Hindi Medium
Free Notes for Ncert class 12 Art अर्थशास्त्र सांख्यिकी Hindi Medium | Free Notes for Ncert class 12 Art इतिहास Hindi Medium | Free Notes for Ncert Class 12 Art समाजशास्त्र Hindi Medium | Free Notes for Ncert Class 12 Art भूगोल Hindi Medium | Free Notes for NCERT Class 12 Art राजनीति विज्ञान Hindi Medium | Free Notes for NCERT Class 12 Art हिन्दी Hindi Medium | Free Notes for NCERT Class 12 Art अंग्रेज़ी Hindi Medium | Free Notes for NCERT Class 12 Art शारीरिक शिक्षा Hindi Medium | Free Notes for NCERT Class 12 Art गृह विज्ञान Hindi Medium | Free Notes for NCERT Class 12 Art समष्टि अर्थशास्त्र Hindi Medium | Free Notes for NCERT Class 12 Art भारतीय अर्थव्यवस्था का विकास Hindi Medium
Free Notes for NCERT class 12 Commerce English Medium
Free Notes for Ncert class 12 Commerce Physical Education | Free Notes for NCERT Class 12 Commerce English | Free Notes for Ncert class 12 Commerce Accountancy | Free MCQ for Ncert Class 12 Commerce Accountancy | Free Notes for NCERT Class 12 Commerce Entrepreneurship | Free Notes for Ncert Class 12 Commerce Economics Micro-Economics | Free MCQ for Ncert Class 12 Commerce Economics Micro-Economics | Free Notes for NCERT Class 12 Commerce Indian Economic Development | Free MCQ for NCERT Class 12 Commerce Indian Economic Development | Free Notes for NCERT Class 12 Commerce Business Studies | Free MCQ for NCERT Class 12 Commerce Business Studies
Free Notes for NCERT class 12 Commerce Hindi Medium
Free Notes for NCERT Class 12 Commerce व्यवसाय अध्ययन | Free Notes for Ncert class 12 Commerce अंग्रेज़ी | Free Notes for NCERT Class 12 Commerce हिंदी | Free Notes for Ncert Class 12 Commerce अर्थशास्त्र सांख्यिकी | Free Notes for NCERT Class 12 Commerce लेखाशास्त्र | Free Notes for NCERT Class 12 Commerce गणित