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

Exercise 8.2 from Class 6 Maths 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 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. 

2.0Key Concepts Covered in Exercise 8.2 Class 6 Maths

• Constructing on dot grid: Using grid points as reference to draw geometric shapes accurately.

• Identifying squares visually: Recognising squares on a grid by observing equal sides and right angles.

• Equal sides and right angles: Verifying that all sides are equal and each angle measures 90°.

• Rotated squares and rectangles: Drawing shapes tilted or rotated while maintaining their geometric properties.

• Verifying geometric properties: Checking side lengths and angles to confirm whether a shape is a square or rectangle.

3.0NCERT Exercise Solutions Class 6 Maths Chapter 8 Playing with Constructions : All Exercises 

4.0NCERT 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.

5.0Key Features and Benefits Class 6 Maths Chapter 8 Playing with Constructions : Exercise 8.2

• Provides a clear step-by-step approach to solving geometric construction problems.
• Helps students learn how to use a compass, ruler, and other geometry tools correctly.
• Improves understanding of basic construction techniques through simple and guided questions.
• Develops spatial visualization and logical reasoning skills in geometry.
• Step-wise solutions make it easier for students to follow the correct construction process.
• Supports preparation for school exams while strengthening basic geometry concepts.