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NCERT Solutions for Class 7 Maths Chapter 10 – Practical Geometry

NCERT Solutions for Class 7 Maths Chapter 10 teaches you to draw parallel lines and different types of triangles in depth. In this chapter, there are 4 exercises and a total of 16 questions. The Chapter of NCERT Solutions for Class 7 Maths – Practical Geometry covers the construction of parallel lines and triangles.  This is a short chapter as compared to other chapters of CBSE Class 7 Maths.

Class 7 NCERT Solutions for Chapter 10 ‘Practical Geometry’ is based on the latest syllabus approved by CBSE. At Instasolve, we provide Chapter-wise Solutions of NCERT Class 7 Maths Book Instasolv helps you in understanding the concepts better and to score high marks in the exams.

Chapter 10 Practical Geometry, of CBSE NCERT Class 7 Maths Book is about the construction of diagrams. For the Maths subject in Class 7, we explain the important elements and summarise each part and subpart of the Chapter. We follow the same sequence as in the book so that it becomes easy to understand and use.

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry: Exercise Discussion

CBSE Class 7 Maths Chapter 10 Introduction

In this chapter, you will learn to draw parallel and different types of triangles. There are several questions based on the topic- Parallel Triangles, which are scoring and easy to solve.

Through NCERT Solutions for Class 7 Maths Chapter 10, you can access easy solutions to each question available in the exercises. 

Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
Recollect the transversal and parallel lines studied earlier. Use of the properties studied and construct a parallel with the help of a ruler and compass. 

  • Draw a line L. Mark a point A away from the line and a point B on the line. Join AB.
  • With B as the center point, use the compass and draw an arc which cuts the line L and AB. This is an angle let us say LAB formed between line L and AB. If on the opposite side we can form the same angle, then the line through A having opposite angles as equal will be parallel to line L
  • Without changing the radius on the compass, make an arc with point A as center cutting AB.
  • Place the pointed tip of the compass on the arc LAB at the point where it cuts line L. The sharpened tip of the pencil should now be placed on the arc LAB at the point where it cuts AB. We have made an arc with point A as the center already. On this arc on the opposite side of angle LAB cut the same angle by placing the compass tip on the point where the arc is cutting line AB and pencil tip cutting the arc to form a new point say D. 
  • Draw a line through points A and D. This line will be parallel to line L.
  • In this Chapter, we will solve questions based on the topic discussed above. To get simple and easy-to-understand solutions, you can refer to our NCERT Maths  Solutions for Class 7 Chapter 1.

Construction of Triangles

In CBSE Class 7 Chapter 10, we will also study deeply about ‘Congruence of Triangles’. We saw that a triangle can be drawn if any one of the following sets of measurements is given: 

– Three sides. (SSS Criterion)

– Two sides and the angle between them. (SAS Criterion)

– Two angles and the side between them. (ASA Criterion)

– The hypotenuse and a leg in the case of a right-angled triangle. (RHS Criterion)

We will now use these ideas to construct triangles. You can refer to NCERT Solutions for Class 7 Maths Chapter 10 by Instasolv, which are 100% accurate and are prepared by our subject matter experts.

Constructing a Triangle when the Lengths of its three Sides are Known (SSS Criterion)

Suppose you have been given three lengths x, y, and z. Whatever is the unit be it centimeter or an inch or meter and so on, you should mention according to the question.

– Take any one side and draw it. It is recommended to take the longest length and draw it first. Suppose you have chosen length z and drawn a line of length z. 

– Use the compass and make an arc of radius equal to length x from one end of the already drawn line. Similarly, draw an arc of radius equal to the lengthy from the other end of the dawn line cutting the previous arc. 

– The intersection point is the third vertex of the triangle. Join the lines from the vertex to the ending points of the already drawn line.

To solve various questions based on SSS Criterion, you can refer to our NCERT Solutions for CBSE Class 7 Maths Chapter 10. You will find all the exercise-wise questions with comprehensive answers here.

Constructing a Triangle when the Lengths of Two Sides and the Measure of the Angle in Between are known (SAS Criterion) 

– First, draw a line of the longest length that is given

– Now from one endpoint of this line make a line of the angle given. You can use a protractor for the same or any other method to make angles.

– On this line mark the length of the second line which has already been given, This point is the third vertex.

– Join the third vertex with the other endpoint of the first line drawn. 

Constructing a Triangle when the Measures of Two of its Angles and the Length on the Side included Between Them is given (ASA Criterion)

First, draw a line of the length given.

– From one endpoint of this line make a line of the measure of the first angle given

– From the second endpoint of this line make a line of the measure of the second angle given

– The two lines of the given angles will intersect at the third vertex of the triangle.

Constructing a Right Angled Triangle when the Length of one Leg and its Hypotenuse are Given (RHS Criterion)

Other than SSS, SAS, ASA, in Chapter 10, we will also study about RHS Criterion in detail.

In this case, we know the length of the longest side which is the hypotenuse. We also know that the right angle is opposite to the hypotenuse. 

– First, draw the leg of the right-angled triangle. This is the length other than that of the hypotenuse. 

– From one endpoint of this leg make a perpendicular line or a line at ninety degrees. This is the right angle of the triangle.

– From the other endpoint of the leg, using a compass and a radius equal to the length of the hypotenuse, make an arc cutting the perpendicular line just drawn. The intersection point is the third vertex. 

– Join the second endpoint to the third vertex to get the hypotenuse of the right-angled triangle.

Study Tips for NCERT Class 7 Maths  Chapter 10: Practical Geometry  

  • As a student, you aim to get a high score in the exams. Instasolv recommends that you read chapter 10 Congruence of Triangles of CBSE NCERT textbook for Class 7 Maths. 
  • Instasolv has provided a simple explanation and a summary of the method of constructing the parallel lines and triangles as given in the NCERT textbook. 
  • Learning by rote is never recommended by our Maths Teachers. This is a simple Chapter and the construction of the diagrams are easy to understand and draw. Ensure you have a good geometry box with sharpened pencils. 
  • Practice for practical geometry class 7 questions and answers will help improve your speed as well Follow the solutions and tips provided by Instasolv and score high marks in your Maths exam.