NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

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# NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

Edited By Ravindra Pindel | Updated on Aug 16, 2023 10:20 AM IST

## NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry - Free CBSE PDF

NCERT Practical Geometry class 7th: The word geometry comprises of two greek words geo and metron. Geo means earth and metron means measurements. Geometry is applied in everyday life from designing simple things like your furniture, doors and windows, the wall clock to the design of complex structures like the designing of a new house. To design all the above structures you need to know about geometry. In CBSE NCERT solutions for Class 7 Maths chapter 10 Practical Geometry, you will get questions related to applications of geometry in real life. You will study a few rulers and compass constructions in this chapter. You will learn how to draw a parallel line to a given line through a point outside the line, how to construct triangles if three sides of triangle are given (SSS), how to construct a triangle if measure of two sides and the angle between them are given (SAS), how to draw a triangle if value of two angles and the length of side included between them are given (ASA), how to draw a triangle if length of hypotenuse and the measure of one leg of a right-angled triangle are given (RHS). There are practice questions given on all the above topics in the .

You should try to solve all these questions by yourself. You can take help from . While solving the problems learn the steps and draw the figures. Just only going through the steps of drawings may not help in the exams. If you have tried to draw all the figures mentioned in the solutions of NCERT for Class 7 Maths chapter 10 Practical Geometry it will be easy for you solve all the questions in the exam related to this chapter. You can get NCERT Solutions from Classes 6 to 12 for Science and Maths by clicking on the above link. Here you will get solutions to five exercises of this chapter.

## NCERT Solutions for Maths Chapter 10 Practical Geometry Class 7th- Important Formulae

Criteria for Congruence of Triangles:

• SSS Congruence: For triangles ABC and DEF, If AB = DE, BC = EF, and AC = DF, Then △ABC ≅ △DEF.

• SAS Congruence: For triangles ABC and DEF, If AB = DE, ∠BAC = ∠EDF, and BC = EF, Then △ABC ≅ △DEF.

• ASA Congruence: For triangles ABC and DEF, If ∠BAC = ∠EDF, ∠ABC = ∠DEF, and AC = DF, Then △ABC ≅ △DEF.

• AAS Congruence: For triangles ABC and DEF, If ∠BAC = ∠EDF, ∠ACB = ∠EFD, and BC = EF, Then △ABC ≅ △DEF.

• RHS Congruence: For right-angled triangles ABC and DEF, If ∠CAB = ∠FDE, AC = DF, and BC = EF, Then △ABC ≅ △DEF.

For more, Download Ebook - NCERT Class 7 Maths: Chapterwise Important Formulas And Points

## NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry - Important Points

Five Measurements Determine a Quadrilateral:

A quadrilateral can be uniquely determined when five measurements related to its sides and angles are known.

Construction with Four Sides and a Diagonal:

If the lengths of all four sides and one diagonal of a quadrilateral are given, the quadrilateral can be constructed uniquely.

Construction with Diagonals and Three Sides:

When the lengths of both diagonals and three sides of a quadrilateral are known, the quadrilateral can be constructed uniquely.

Construction with Adjacent Sides and Angles:

If the lengths of two adjacent sides and the measures of three angles of a quadrilateral are provided, the quadrilateral can be constructed uniquely.

Construction with Three Sides and Included Angles:

If the lengths of three sides and the measures of two angles included between those sides are given, the quadrilateral can be constructed uniquely.

Free download NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry PDF for CBSE Exam.

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## NCERT Solutions for Maths Chapter 10 Practical Geometry Class 7th Exercise 10.1

Answer:

1. Draw the line AB

2. Mark any point C outside AB and a point D on AB

3. Join CD

4. Draw an arc with convenient radius with D as centre cutting AB at E and DC at F

5. With the same radius as in step 4 draw an arc IGH with C as a centre and cutting line AC at G.

6 Place one tip of the compass on E and adjust the opening so that pencil tip touches at F.

7. With the same opening in step 6 and G as centre cut an arc at J on IGH.

8. Join CJ and extend the line. This line will be parallel to AB

Answer:

1. Draw a line l. Mark a point P on the line

2. With p as a centre and with any radius draw an arc which touches the line at A and B

3. Take a length more than AP with A as centre draw an arc. with the same length on compass and B as centre draw an arc to cut the previous arc at Q.

4. Join PQ. PQ is perpendicular to the line l

5. Take 4 cm on the compass and with P as centre cut an arc on line PQ at C. The length PC=4 cm

6. with P as a centre and any radius, draw an arc to cut line l at D and PQ at E.

7. with the same radius as in step 6 draw an arc GF with centre C so that it cuts the line PQ at G.

8. Take the length DE on the compass and with G as centre draw an arc to cut FG at J

9. Join CJ and extend the line to name it as line m. Now the line l is parallel to line m

Answer:

1. Draw the line PQ parallel to l using the steps to draw parallel lines

2. Draw the line RS parallel to PQ using the steps to draw parallel lines

the two parallel lines make the shape of a parallelogram PQRS.

## NCERT Solutions for Maths Chapter 10 Practical Geometry Class 7th Exercise 10.2

Answer:

$\Delta XYZ$ in which XY= 4.5 cm, YZ = 5 cm and ZX = 6 cm :

1. Draw a line XY = 4.5 cm

2. with x as centre and length= 6cm draw an arc

3. with y as centre and length = 5cm draw another arc to cut the arc drawn in step 2 at Z

4. Join XZ and YZ. XYZ is the required triangle

Answer:

an equilateral triangle of side 5.5 cm :

1. Draw a line AB = 5.5 cm

2. with A as centre and length= 5.5cm draw an arc

3. with B as centre and length = 5.5cm draw another arc to cut the arc drawn in step 2 at C

4. Join AC and BC.ABC is the required triangle

Answer:

PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm:

1.Draw a line QR = 3.5 cm

2. With Q as centre and length = 4 cm draw an arc

3. With R as centre and length = 4cm draw another arc to cut the previous arc at P

4. Join QP and QR. Then PQR is the required triangle

As we can see two sides of the triangle are same so The triangle is an isosceles triangle.

Answer:

$\Delta ABC$ such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure $\angle B$ :

1. Draw a line AB = 2.5 cm

2. with A as centre and length= 6.5cm draw an arc

3. with B as centre and length = 6cm draw another arc to cut the arc drawn in step 2 at C

4. Join AC and BC. ABC is the required triangle

On measuring angle B comes out to be 90 degrees.

## NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Exercise 10.3

Answer:

$\Delta DEF$ such that DE = 5 cm, DF = 3 cm and $m\angle EDF=90^{\circ}$ :

1. Draw a line DE = 5cm

2. Draw a line DX making 90 degrees with DE.

3. cut the length DF =3cm using the compass on the line DX

4. Join E and F

DEF is the required triangle

Answer:

1. Draw a line DE = 6.5 cm

2. Draw a line DX making 110 degrees with DE.

3. cut the length DF =6.5 cm using the compass on the line DX

4. Join E and F

DEF is the required triangle

Answer:

$\Delta ABC$ with BC = 7.5 cm, AC = 5 cm and $m\angle C=60^{\circ}$ :

1. Draw a line AC = 5 cm

2. Draw a line CX making 60 degrees with AC from C.

3. cut the length BC =7.5 cm using the compass on line CX

4. Join A and B

ABC is the required triangle

## NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Exercise 10.4

Answer:

$\Delta ABC$ , given $m\angle A=60^{\circ}$ , $m\angle B=30^{\circ}$ and AB = 5.8 cm :

1. Draw the line AB=5.8 cm

2. At A making an angle 60 degrees with AB draw a line AX

3. At B making an angle 30 degrees with AB draw a line BY

4. The lines AX and BY intersect at C ( in case the drawn line AX or BY is small extend it to intersect each other)

ABC is the requires triangle

Answer:

$\Delta PQR$ if PQ = 5 cm, $m\angle PQR = 105^{\circ}$ and $m\angle QRP = 40^{\circ}$ :

the sum of angles of a triangle is 180 degrees. Given angles PQR and QRP, so the angle QPR= 180-(105+40)=35 degrees

1. Draw the line PQ=5 cm

2. At Q making an angle 105 degrees with PQ draw a line QY

3. At P making an angle 35 degrees with PQ draw a line PX

4. The lines PX and QY intersect at R ( in case the drawn line PX or QY is small extend it to intersect each other)

PQR is the required triangle

Answer:

No, we cannot construct such that EF = 7.2 cm, $m\angle E = 110^{\circ}$ and $m\angle F = 80^{\circ}$ . This is because of the property of the triangle of having a sum of internal angles equal to 180 degrees. if we have $m\angle E = 110^{\circ}$ , then we cannot have $m\angle F = 80^{\circ}$ because then the sum would exceed 180 degree which is impossible.

## NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Exercise 10.5

Answer:

the right-angled $\Delta PQR$ , where $\angle Q=90^{\circ}$ , QR = 8cm and PR = 10 cm:

1. Draw QR = 8 cm

2. Draw a perpendicular QX to QR at Q

3. From R and with length = 10 cm cut an arc on QX. The arc meet QX at P

4. Join PR

PQR is the required triangle

Answer:

a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long:

1. Draw QR = 4 cm

2. Draw a perpendicular QX to QR at Q

3. From R and with length = 6 cm cut an arc on QX. The arc meet QX at P

4. Join PR

Triangle PQR is the required triangle

Answer:

1. Draw CA = 6 cm

2. Draw a perpendicular CX to CA at C

3. From C and with length = 6 cm cut an arc on CX. The arc meet CX at B

4. Join BA

Triangle ABC is the required triangle

## Practical Geometry Class 7 Maths Chapter 10-Topics

• Construction Of A Line Parallel To A Given Line, Through A Point Not On The Line
• Construction Of Triangles
• Constructing A Triangle When The Lengths Of Its Three Sides Are Known (Sss Criterion)
• Constructing A Triangle When The Lengths Of Two Sides And The Measure Of The Angle Between Them Are Known. (Sas Criterion)
• Constructing A Triangle When The Measures Of Two Of Its Angles And The Length Of The Side Included Between Them Is Given. (Asa Criterion)
• Constructing A Right-angled Triangle When The Length Of One Leg And Its Hypotenuse Are Given (Rhs Criterion )

### NCERT Solutions for Class 7 Maths Chapter Wise

 Chapter No. Chapter Name Chapter 1 Integers Chapter 2 Fractions and Decimals Chapter 3 Data Handling Chapter 4 Simple Equations Chapter 5 Lines and Angles Chapter 6 The Triangle and its Properties Chapter 7 Congruence of Triangles Chapter 8 Comparing quantities Chapter 9 Rational Numbers Chapter 10 Practical Geometry Chapter 11 Perimeter and Area Chapter 12 Algebraic Expressions Chapter 13 Exponents and Powers Chapter 14 Symmetry Chapter 15 Visualising Solid Shapes

### NCERT Solutions for Class 7 Subject Wise

 NCERT Solutions for Class 7 Maths NCERT Solutions for Class 7 Science

## Some applications of geometry

• Construction works:- For the construction of houses, bridges, buildings, roads, tanks, dams, etc you need to have knowledge of geometry otherwise you cant do these things with better accuracy. In NCERT solutions for class 7 maths chapter 10 practical geometry, you have learnt some basics of geometry which will help you in higher study.
• Games:- In all the computer games or mobile games, you will see particular patterns, maps, 2D and 3D images etc. To designing all these thing you need to have knowledge of geometry.
• Art:- Artist uses the geometry to organise the arrangement of space in a picture.
• Architecture:- Architect use knowledge of geometry to transform the build the material of architectural design.
• Sports:- From designing the pitch, the boundary in cricket to draw the lines in tennis court you need to have knowledge of geometry.

In CBSE NCERT solutions for Class 7 Maths chapter 10 Practical Geometry, you have learnt some fundamental of geometry for simple mathematical geometry. There are many other applications of geometry in the field of designing, civil engineering, CAD(computer-aided design), mapping, GPS and many more which you will learn in higher classes.

Happy Reading!!!

Also Check NCERT Books and NCERT Syllabus here:

### Frequently Asked Question (FAQs)

1. What is practical geometry?

Practical geometry Class 7th is a branch of geometry in which we learn the method of constructing various geometrical shapes like line segments, angles, triangles, and different polygons.  We use various geometrical tools to construct the required shapes with the exact measurements given.

2. How many exercises in NCERT solution Class 7 Maths Chapter 10?

There are 5 exercises in NCERT chapter 10 maths class 7th.

Practical Geometry Class 7 NCERT Exercise 10.1- 3 questions

Practical Geometry Class 7th NCERT Exercise 10.2- 4 questions

Practical Geometry Class 7th NCERT Exercise Exercise 10.3 - 3 questions

Practical Geometry Class 7 NCERT Exercise 10.4 - 3 questions

Practical Geometry Class 7th NCERT Exercise Exercise 10.5 - 3 questions

3. Who is the father of geometry?

The Father of Geometry is  Euclid. He was a Greek Mathematician. He discussed many concepts related to Geometry, students can get brief idea from class 7 chapter 10 maths about these concepts. Also you can practice practical geometry class 7 pdf to get deeper understanding of concepts.

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##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
##### Talent Agent

The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

3 Jobs Available
##### Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Music Teacher

Career as a Music Teacher is a fun and exciting job if you are skilled and passionate about this career. A Music Teacher is responsible for teaching students music, instruments, techniques, technology, singing, and many more. He or she helps students to analyze musical works, and concepts of music and assigns and evaluates lessons.

2 Jobs Available
##### Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### News Anchor

A career as news anchor requires to be working closely with reporters to collect information, broadcast newscasts and interview guests throughout the day. A news anchor job description is to track the latest affairs and present news stories in an insightful, meaningful and impartial manner to the public. A news anchor in India needs to be updated on the news of the day. He or she even works with the news director to pick stories to air, taking into consideration the interests of the viewer.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

3 Jobs Available
##### Videographer

Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

2 Jobs Available
##### SEO Analyst

An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.

2 Jobs Available
##### Gemologist

A career as a gemologist is as magnificent and sparkling as gemstones. A gemologist is a professional who has knowledge and understanding of gemology and he or she applies the same knowledge in his everyday work responsibilities. He or she grades gemstones using various equipment and determines its worth. His or her other work responsibilities involve settling gemstones in jewellery, polishing and examining it.

4 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Production Manager

Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

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3 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

2 Jobs Available
##### Commercial Manager

A Commercial Manager negotiates, advises and secures information about pricing for commercial contracts. He or she is responsible for developing financial plans in order to maximise the business's profitability.

2 Jobs Available
##### QA Manager

Quality Assurance Manager Job Description: A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes.

2 Jobs Available
##### Reliability Engineer

Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment.

2 Jobs Available
##### Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
##### ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### IT Consultant

An IT Consultant is a professional who is also known as a technology consultant. He or she is required to provide consultation to industrial and commercial clients to resolve business and IT problems and acquire optimum growth. An IT consultant can find work by signing up with an IT consultancy firm, or they can work on their own as independent contractors and select the projects they want to work on.

2 Jobs Available
##### Data Architect

A Data Architect role involves formulating the organisational data strategy. It involves data quality, flow of data within the organisation and security of data. The vision of Data Architect provides support to convert business requirements into technical requirements.

2 Jobs Available
##### AI Data Analyst

An AI Data Analyst is responsible for procuring, preparing, cleansing and modelling data utilising machine learning models and new analytical methods. He or she designs and creates data reports in order to provide support to stakeholders to make better decisions.

2 Jobs Available
##### Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.

2 Jobs Available
##### UX Architect

A UX Architect is someone who influences the design processes and its outcomes. He or she possesses a solid understanding of user research, information architecture, interaction design and content strategy.

2 Jobs Available
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