NCERT Solutions for Class 6 Maths Chapter 8 - Playing with Constructions Exercise 8.5

Exercise 8.5

Question 1.
Construct a rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.
Ans: We shall draw a rectangle of the form shown in Fig. 1.

Step 1. Using a ruler, draw a line AB equal to 4 cm, say. (Fig. 2.)

Step 2. Using a protractor, mark dots C and D at angles 50° and 90° (50° + 40°), keeping the central point of the protractor at A. (Fig. 3)

Step 3. Using a protractor, draw a perpendicular line to AB at B and let it intersect the extended line AC at E. (Fig 3)

Step 4. Using a protractor, draw a perpendicular line to BE at E and let it intersect the extended line AD at F. (Fig 4)

Step 5. Erase the extra lines in Fig. 4. (Fig. 5)

Step 6. Fig. 5 is the required rectangle in which one of the diagonals divides the opposite angles into 50° and 40°.

Question 2.
Construct a rectangle in which one of the diagonals divides the opposite angles into 45° and 45°. What do you observe about the sides?
Ans: Do it yourself.

Question 3.
Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Ans: We shall draw a rectangle of the form shown in Fig. 1.

Step 1. Using a ruler, draw a line AB equal to 4 cm. (Fig. 2)

Step 2. Using a protractor, draw a perpendicular line to AB at A and B (Fig. 3)

Step 3. With the centre at A and a radius equal to 8 cm, draw an arc to intersect the perpendicular at B. Similarly, draw an arc of radius 8 cm with a centre at B to intersect perpendicular at A. (Fig. 4)

Step 4. Join the points of intersection of arcs by PQ. (Fig. 5)

Step 5. Erase the extra lines in Fig. 5 (Fig. 6)

Step 6. Fig. 6 is the required rectangle with one side equal to 4 cm and diagonals of length 8 cm.

Question 4.
Construct a rectangle one of whose sides is 3 cm and the diagonal is of length 7 cm.
Ans:

Benefits of NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.5 Playing with Constructions

• The solutions provide a clear explanation of various geometric constructions, helping students grasp the fundamental concepts effectively.

• Each problem is broken down into detailed steps, making it easy for students to follow and replicate the construction techniques accurately. 

• By practising geometric constructions, students develop essential skills in using a compass and ruler, which are vital tools in geometry. 

• The solutions are designed to align with the CBSE Class 6 Maths syllabus, ensuring that all necessary topics related to constructions are covered. 

• Regular practice with these solutions enhances students’ ability to approach and solve geometric problems systematically.

• The exercise encourages visual learning, helping students understand the relationship between different geometric figures and their properties.

• Mastering the techniques of geometric constructions lays a solid foundation for tackling more complex geometry topics in higher classes.

Class 6 Maths Chapter 8: Exercises Breakdown

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

Conclusion

The NCERT Solutions for Class 6 Maths Chapter 8 Exercise 8.5, Playing with Constructions, are an invaluable resource for students seeking to master geometric constructions. With clear, step-by-step guidance and practical applications, these solutions enhance understanding and confidence in using essential tools like a compass and ruler. Aligned with the CBSE syllabus, they provide comprehensive coverage of the necessary concepts, preparing students for more advanced topics in geometry. The availability of FREE PDF downloads ensures easy access for effective study and revision. Overall, these solutions empower students to develop strong foundational skills in geometry, paving the way for future mathematical success. 

Chapter-Specific NCERT Solutions for 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 Maths Class 6

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