NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.2

NCERT Solutions Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.2 is concerned with constructing angles using a compass, constructing perpendicular lines from a point and constructing angle bisectors. Activities of this type will assist students to develop their ability to accuracy, hone their ability to concentrate, and provide useful and productive work to understand geometric principles through processes and practices.

Our NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.2 have clear illustrations and comprehensible step-by-step procedures for each construction.  By using these NCERT Solutions, students are encouraged not only to learn the tactics of dealing with geometric tools and utilize them properly, but it will also help them set a strong basis of knowledge and skill for tackling higher class geometry topics.

1.0Download NCERT Solutions of Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.2: Free PDF

Download the NCERT Solutions for Class 6 Maths Chapter 8 Playing with Constructions Exercise 8.2 in a one-click, downloadable PDF. 

Key Concepts of Exercise 8.2

• Construct an angle with a compass;  
• Draw a perpendicular line to a given point;  
• Construct perpendicular lines at a given point;  
• Construct the angle bisects with a straight edge and compass;  
• Utilize the tools of practical geometry accurately.

2.0NCERT Exercise Solutions Class 6 Maths Chapter 8 Playing with Constructions : All Exercises 

3.0NCERT Class 6 Chapter 8 Playing with Constructions Exercise 8.2 : Detailed Solutions

8.2 Squares And Rectangles

1. Draw the rectangle and four squares configuration (shown below) on a dot paper. What did you do to recreate this figure so that the four squares are placed symmetrically around the rectangle? Discuss with your classmates.
   
   Sol. Step 1: Take a square dot paper and mark a dot on it at A. Start from A move 10 dots to the right and mark the tenth dot at B . Step 2: Start from $B$ and move 6 dots above $B$ and mark the 6th dot as $C$. Start from $A$ and move 6 dots above A and mark the 6th dot as D . Join $\mathrm{AB},\mathrm{BC},\mathrm{CD}$, and DA . Step 3: Take points E, F, G, and H on the dot paper as shown in the figure. Step 4: Take points I, J, K, and L at a distance of 4 dots from E, F, G, and H respectively. Join IE, FJ, GK, and LH. Step 5: On LH and GK, construct squares above the rectangle. Step 6: On IE and FJ, construct squares below the rectangle.
   
   Step 7: The figure is the required configuration of one rectangle and four squares on a square dot paper.
2. Identify if there are any squares in this collection. Use measurements if needed.
   
   Think: Is it possible to reason out if the sides are equal or not, and if the angles are right or not without using any measuring instruments in the above figure? Can we do this by only looking at the position of corners in the dot grid? Sol:
   
   Fig. (i): In this figure, counting dots between sides, we find that $\mathrm{AB},\mathrm{BC},\mathrm{CD}$, and DA are all equal sides. Also, the position of the dots on the sides shows that each angle of ABCD is $90^{\circ }$. $\therefore \mathrm{ABCD}$ is a square. Fig. (ii): In this figure, $\angle \mathrm{BAD}$ is not equal to $90^{\circ }$. So, ABCD cannot be a square. Fig. (iii): In this figure, counting dots between sides, we find that $\mathrm{AB},\mathrm{BC},\mathrm{CD}$, and DA are all equal sides. Also, using a protractor, we find that each angle of ABCD is $90^{\circ }$. $\therefore \mathrm{ABCD}$ is a square. Fig. (iv): In this figure, AB and BC are not equal. So, ABCD cannot be a square.
3. Draw at least 3 rotated squares and rectangles on a dot grid. Draw them such that their corners are on the dots. Verify if the squares and rectangles that you have drawn satisfy their respective properties. Sol. We draw 3 rotated squares and rotated rectangles on a dot grid such that the comers of squares and rectangles are on dots.
   
   We have drawn 3 rotated squares (ii and iii) and rotated rectangles (i). These squares and rectangles are drawn keeping in view the number of dots between sides and also the position of sides. Using a ruler, we find that the opposite sides of figures (i) are equal and all sides of figures (ii), (iii), (iv) are equal. $\therefore$ By definition, figures (i) is rectangles, and figures (ii) and (iii), (iv) are squares.

4.0Key Features and Benefits Class 6 Maths Chapter 8 Playing with Constructions : Exercise 8.2

• Step by step guide through all the constructions;  
• Visual pictures to exhibit how to use tools of geometry;  
• Clear cut explanation of each rule and method;  
• Acquires spatial reasoning and logical reasoning skills;  
• Will assist students for both school exams and practice.