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

Exercise 8.2

1. Draw the rectangle and four squares configuration (shown in Fig. 8.3) 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.

Ans:

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 AB, BC, 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?

Ans:

Fig. I: In this figure, AB and BC are not equal. So, ABCD cannot be a square.
Fig. II: In this figure, ∠BAD is not equal to 90°. So, ABCD cannot be a square.
Fig. III: In this figure, counting dots between sides, we find that AB, BC, CD, and DA are all equal sides. Also, the position of the dots on the sides shows, that each angle of ABCD is 90°.
∴ ABCD is a square.
Fig. IV: In this figure, counting dots between sides, we find that AB, BC, CD, and DA are all equal sides. Also, using a protractor, we find that each angle of ABCD is 90°.
∴ ABCD is 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.

Ans: We draw two rotated squares and two rotated rectangles on a dot grid such that the comers of squares and rectangles are on dots.

We have drawn two rotated squares (II and III) and two rotated rectangles (I and IV). These squares and rectangles are drawn keeping in view the number of dots between sides and also the position of sides.

Using a protractor, we find that all angles of figures I to IV are 90°.

Using a ruler, we find that the opposite sides of Figures I and IV are equal and all sides of Figures II and III are equal.

∴ By definition, figures I and IV are rectangles, and figures II and III are squares.

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

• The solutions provide step-by-step guidance on constructing squares and rectangles, making complex concepts easy to understand.

• Diagrams and illustrations help students visualize geometric constructions, enhancing their spatial reasoning skills.

• Students can practice various problems, reinforcing their learning and boosting their confidence in geometry.

• The solutions align with the NCERT syllabus, helping students prepare effectively for exams with relevant exercises.

• Engaging with these solutions encourages critical thinking and improves problem-solving abilities through hands-on construction tasks.

• Available in a FREE PDF format, these solutions can be easily downloaded and accessed anytime, supporting flexible study schedules.

Class 6 Maths Chapter 8: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 8 - Playing with Constructions

Conclusion

NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.2, "Playing with Constructions," serve as an invaluable resource for students. By providing clear, step-by-step guidance on constructing squares and rectangles, these solutions enhance understanding and boost confidence in geometric concepts. They offer ample practice opportunities, crucial for effective exam preparation, while also fostering critical thinking and problem-solving skills. Accessible in a FREE PDF format, these solutions support students in their learning journey, making geometry engaging and approachable. Explore these solutions to strengthen your foundation in mathematics and excel in your studies!

Chapter-wise NCERT Solutions Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Class 6  Maths 

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.