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NCERT Solutions for Class 9 Maths Chapter 11 Constructions

With NCERT Solutions for Class 9 Maths Chapter 11 Constructions, every student can achieve full marks in this chapter. Do you know how? Chapter 11 Constructions is a scoring chapter in Class 9 Maths. It is based on the construction of perpendicular bisectors, bisectors, and triangles. You just have to remember the steps and you will be able to solve the questions easily. 

NCERT Solutions for Class 9 Maths provide all the answers to you for exercises 11.1 and 11.2. The stepwise constructions are done to help you understand how you have to solve the questions in your examination. You can download the PDF answers for the Class 9 Maths Constructions chapter for free and use them for practice. 

About NCERT Solutions for Class 9 Maths Chapter 11 Constructions

In Chapter 11 of Class 9 Maths NCERT book, you have to use a ruler and compass to construct different angles, their perpendicular bisectors and bisectors. You will also learn how to construct a triangle when its base, base angle and the sum of its two sides are given to you. Here are a few tips that will help you solve the NCERT exercises of this chapter easily.

Steps to construct the bisector of a given angle:

  • Consider an angle AOB. Taking O as a centre and any radius, draw an arc to intersect the rays BA and BC, say at Y and X respectively. 
  • Taking Y and X as centres and with a radius more than XY, draw arcs to intersect each other, say at C.
  • Draw the ray BC. This ray BC is the required bisector of the angle ABC.

Steps to construct a perpendicular bisector:

  • To create a perpendicular bisector of a line segment AB, take A and B as the centres and radius more than 1/2 of Ab and draw the arcs on both sides.
  • The arcs would intersect each other at C and D. And join CD.
  • Here CD intersects AB at point M so that M is the midpoint of AB and CMD is the required perpendicular bisector of AB.

Steps to construct a triangle if its base, a base angle and sum of other two sides are given:

  • Draw the base BC and at point B makes an∠XBC equal to the given angle.
  • From the ray BX, cut the line segment BD = AB + AC.
  • Join DC now which make ∠DCY = ∠BDC.
  • When CY intersect BX at A then it forms the required triangle i.e. ABC.

Steps to construct a triangle if its base, a base angle and the difference of the other two sides are given:

If AB > AC that is AB – AC is given, then

  • Draw the base BC which is equal to a cm and at point B make an∠XBC = x°.
  • From the ray BX, cut the line segment BD which is equal to AB – AC.
  • Join DC and draw the perpendicular bisector of DC.
  • This perpendicular bisector intersects BX at point A. By joining A to C we get the required triangle i.e. ∆ABC.

If AB < AC that is AC – AB is given, then

  • Draw the base BC and at point B make an ∠XBC.
  • From ray, BX cut the line segment BD which is equal to AC – AB from the line BX by extending it on the opposite side of line segment BC.
  • Join DC and draw the perpendicular bisector of DC.
  • Let PQ intersect BX at A and by joining A to C, we get the required triangle ∆ABC.

Download NCERT Solutions for Class 9 Maths Chapter 11 Constructions for FREE

Chapter 11 of the grade 9 NCERT textbook includes two exercises. Exercise 9.1 has 5 questions and exercise 9.2 also has 5 questions based on constructing angle bisectors, perpendicular bisectors, and triangles. Download the PDF version of NCERT solutions for Class 9 Maths Chapter 11 Constructions for free and start practising:

NCERT Class 9 Chapter 11 Ex 11.1 Solutions - 5 Questions 

NCERT Class 9 Chapter 11 Ex 11.2 Solutions - 5 Questions

NCERT Solutions for Class 9 Maths Chapter 11 Ex 11.1 

The first exercise of this chapter is based on how to construct an angle bisector, perpendicular bisector and an angle of 600 at the initial point of a given ray. There are just 5 questions in the exercise that we have solved step by step for you in our NCERT free solutions. This will help you get familiar with how to solve construction problems in the exam and you can prepare yourself accordingly. 

NCERT Solutions for Class 9 Maths Chapter 11 Ex 11.2 

The second exercise of this chapter deals with the construction of triangles when:

  • Its base, a base angle and sum of the other two sides is given. 
  • Its base, a base angle and the difference of the other two sides is given. 
  • Its perimeter and its two base angles are given. 

You can check how to construct triangles in our NCERT answers for Chapter 11 Constructions. We are sure you will be able to understand the steps of construction easily as we have drawn diagrams for every corresponding step. 

NCERT Solutions for Class 9 Maths Chapter 11 Constructions FAQs

  1. Do I need to practice every NCERT exercise question for the Constructions chapter? 

Yes, you must practice all the questions for conceptual clarity and understanding. This will help you score full marks in this chapter in exams. 

  1. Are these NCERT Solutions by askIITians for Class 9 Maths Chapter 11 reliable? 

All these solutions are prepared by our Maths experts who have years of experience in reaching NCERT concepts to students. We check the solutions thoroughly before providing them to you and ensure that all the answers are correct and based on the latest syllabus. 


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