CTET & State TET Exam  >  CTET & State TET Notes  >  Mathematics & Pedagogy  >  Exercise 11.2 NCERT Solutions - Constructions

NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions

Q1. Construct a triangle ABC in which BC = 7 cm, ∠B = 75º and AB + AC = 13 cm.
Ans: Steps of construction:

  • Draw a ray BX.
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions cut off NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions = 7 cm.
  • At B, construct ∠CBY = 75º.
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions cut off BD = 13 cm (= AB + BC)NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions
  • Join D and C.
  • Bisect DC such that the bisector of DC meets BD at A.
  • Join AC.

Thus, ΔABC is the required triangle.


Q2. Construct a triangle ABC in which BC = 8 cm, ∠ B = 45º and AB ∠ AC = 3.5 cm.
Ans: Steps of construction: 

  • Draw a ray NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions , cut off BC = 8 cm.
  • Construct ∠CBY = 45º.
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions cut off NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions = 3.5 cm.
    NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions
  • Join D and C.
  • Draw PQ, the perpendicular bisector of DC, which intersects NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions at A.
  • Join AC.

Thus, ABC is the required triangle.


Q3. Construct a triangle PQR in which QR = 6 cm, ∠Q = 60º and PR ∠ PQ = 2cm.
Ans: Steps of construction:

  • Draw a ray NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions .
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions, cut off QR = 6 cm.
  • Construct a line YQY' such that ∠RQY = 60º.
    NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions
  • Cut off QS = 2 cm (from QY').
  • Join ‘S’ and ‘R’.
  • Draw MN, the perpendicular bisector of SR, which intersects QY at P.
  • Join P and R.

Thus, PQR is the required triangle.


Q4. Construct a triangle XYZ in which ∠ Y = 30º , ∠ Z = 90º and XY + YZ + ZX = 11 cm.
Ans: Steps of construction:

NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions

  • Draw a line segment AB = 11 cm = (XY + YZ + ZX)
  • Construct ∠BAP = 30º = ∠Y
  • Construct ∠ABQ = 90º = ∠Z
  • Draw NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions , the bisector of ∠BAP.
  • Draw NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions , the bisector of ∠ABQ, such that NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions and NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions intersect each other at X.
  • Draw perpendicular bisector of AX, which intersects AB at Y.
  • Draw perpendicular bisector of XB, which intersects AB at Z.
  • Join XY and XZ.

Thus, XYZ is the required triangle.

 

Q5. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.
Ans: Steps of construction:

  • Draw NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions = 12 cm.
  • Construct ∠CBY = 90º.NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions
  • From NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions cut off BX = 18 cm.
  • Join CX.
  • Draw PQ, the perpendicular bisector of CX, such that PQ meets BX at A.
  • Join AC.

Thus, ABC is the required triangle.

The document NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions is a part of the CTET & State TET Course Mathematics & Pedagogy.
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FAQs on NCERT Solutions for Class 6 Maths - Exercise 11.2 Constructions

1. What is the significance of Exercise 11.2 in NCERT Solutions - Constructions?
Ans. Exercise 11.2 in NCERT Solutions - Constructions is a practice exercise that focuses on construction problems related to various geometrical figures. It helps students enhance their skills in constructing different shapes accurately using a compass, ruler, and other geometric tools.
2. How can Exercise 11.2 in NCERT Solutions - Constructions help me in my exams?
Ans. Exercise 11.2 in NCERT Solutions - Constructions provides a wide range of construction problems that are frequently asked in exams. By practicing these problems, students can familiarize themselves with the construction techniques and gain confidence in solving similar questions in their exams.
3. Are the solutions provided for Exercise 11.2 in NCERT Solutions - Constructions easy to understand?
Ans. Yes, the solutions provided for Exercise 11.2 in NCERT Solutions - Constructions are designed to be easily understandable. Each step is explained in a detailed and systematic manner, making it easier for students to follow the construction process and replicate it effectively.
4. Can I use Exercise 11.2 in NCERT Solutions - Constructions for self-study?
Ans. Absolutely! Exercise 11.2 in NCERT Solutions - Constructions is a valuable resource for self-study. It offers a variety of construction problems along with step-by-step solutions, allowing students to practice and improve their construction skills independently.
5. How can I make the most out of Exercise 11.2 in NCERT Solutions - Constructions?
Ans. To make the most out of Exercise 11.2 in NCERT Solutions - Constructions, it is recommended to thoroughly understand the construction techniques explained in the textbook. Practice each problem multiple times and ensure you can accurately construct the given figures. Additionally, try to solve similar construction problems from other sources to further strengthen your skills.
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