# NCERT Solutions for Class 9 Maths Chapter 11 Constructions (Ex 11.1) Exercise 11.1

Students can find the solutions for Exercise 11.1 of Class 9 Mathematics Chapter 11 in the NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 prepared by experienced teachers following the guidelines of the NCERT. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 can assist students with regard to understanding the entire syllabus and securing more marks. They can download NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 from the Extramarks educational website. Students can access the solutions to Exercise 11.1 Class 9 Maths from the Extramarks e-learning portal.

## NCERT Solutions for Class 9 Maths Chapter 11 Constructions (Ex 11.1) Exercise 11.1

Extramarks offers PDF downloads of NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1  are developed by subject matter experts with deep knowledge and extensive experience. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 have been developed according to the latest NCERT guidelines and examination templates, making them a reliable resource for examination preparation. Students can also download the NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 as a PDF and use them for revision. Of the most accessible online materials available for the Class 9 Mathematics curriculum, the NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 could be considered one of the most reliable resources to practice for the Class 9 annual exams. Students can get the NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 to help solve problems given in the Maths Class 9 Chapter 11 Exercise 11.1 textbook.

### Access NCERT Solutions for Class-9 Maths Chapter 11 – Construction

In the prescribed NCERT textbook of Mathematics for Class 9, Construction is Chapter 11. In this chapter, students will learn the required measurement angles and methodology for accurately constructing various 2D shapes. Students will learn in Class 9 Maths Exercise 11.1 Solutions how to use compasses, protractors, dividers, and squares. It is imperative that they practice NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 progressively and thoroughly.

In addition, students will become familiar with the types and patterns of questions that will appear in the examinations with the help of NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1. The NCERT book itself contains numerous questions of varying difficulty that assess students’ understanding of concepts.

### NCERT Solution Class 9 Maths of Chapter 11 All Exercises

A basic understanding of these concepts is very important for students, as they form the basis of advanced mathematical studies, particularly Trigonometry, Calculus, And Coordinate Geometry. All the concepts are easily explained in NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1.

### NCERT Solutions for Class 9 Maths Chapter 11 Constructions Exercise 11.1

Students can learn how to bisect a straight line and how to create specific angles using a compass and ruler with the help of  NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1.

### NCERT Solutions for Class 9

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### CBSE Study Materials for Class 9

The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 are most important to students. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 have been compiled in consideration of the nuances of the prescribed mathematics syllabus for Class 9. Additionally, NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 provide students with an excellent learning foundation. On Extramarks, students can conveniently access PDF versions of NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1.

Extramarks provides NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 along with solutions for all subjects like Social Studies, Mathematics, Science, Hindi and English. To do well on examinations, students need to study each subject thoroughly. NCERT Solutions for Class 9 for each subject in Class 9 will help them perform well in exams. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 consist of all the solutions to the questions provided in Exercise 11.1 cover all the topics and key points present. There are a total of 15 chapters in the curriculum of Class 9 Mathematics.

### CBSE Study Materials

Class 9 Mathematics Chapter 1

In this chapter, students will also learn how to place different types of numbers on the number line. Chapter 1 in 9 Class also focuses on where to place the square roots of 2 and 3 on the number line, rational numbers, the law of rational exponents, and integer powers. Some of the topics covered in this chapter are Decimal Endings and Their Examples, Rational Zeros, Rationalisations, and Exponential Laws. they need to learn about Natural Numbers, Integers, Integers, etc. Students could also explore the properties and characteristics of Rational and Irrational Numbers.

Class 9 Mathematics Chapter 2

This chapter describes algebraic expressions for polynomials and related terms. This chapter provides definitions and examples of polynomials, as well as coefficients, degrees, and terms used in polynomials. Chapter 2 of NCERT Class 9 also focuses on different forms of polynomials, such as Quadratic Polynomials, Linear Constants, Cubic Polynomials, The Factorization Theorem, and the Factorisation Theorem. Students can also solve additional 9 ​​Class Mathematics problems in NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1.

Class 9 Mathematics Chapter 3

In Chapter 3 of 9 Class Mathematics, students will learn how to graph linear equations and find solutions to two-variable linear equations. Students should practise the questions in this chapter and understand the formulas. Using graphing, they would learn to draw a linear equation with two variables. Students should carefully study the following topics in this chapter. Students should practice and review the examples before starting the exercises.

Class 9 Mathematics Chapter 4

This chapter has three exercises that students can use to learn more about Coordinate Geometry. In this chapter, students will learn some terms related to the Cartesian plane and the Coordinate plane. Students will also learn how to draw a point in the XY plane and give it a name. This chapter is very important, and some of the topics covered in it are Cartesian Coordinates, Coordinates of a Point, Plotting Points on a Plane, etc. Students would learn to write dots in different quadrants, signs of quadrants, and more. Students would also need to learn how to plot a graph and a point on the Cartesian plane. Students should attempt to solve as many questions as they can and practice the examples.

Class 9 Mathematics Chapter 5-Introduction to Euclidean Geometry

This chapter introduces different geometrical terms and shapes. This chapter has 2 exercises that require learning theorems: the axioms and the relationship between the axioms. Students must be able to prove the relationship between axioms and theorems. Students are advised to learn all the assumptions and theorems. Students should pursue examples to better understand the concept. This chapter is very easy, and they can get a good score.

Lines and Angles NCERT Class 9 Mathematics Chapter 6

Class 9 Mathematics Chapter 6, has some theorems and their proofs based on angles and lines. A postulate covered in this chapter is that the sum of the angles in a triangle is always 180°, and the sum of two opposite interior angles gives an exterior angle. Students must be extremely careful when reading this chapter. All exercise problems should be addressed and practised. Topics like Linear Vs. Lines Parallel to the Same Line are some of the basic topics of this chapter. Students would learn the shapes and properties of Angles and Triangles.

Class 9 Mathematics Chapter 7

Class 9 Mathematics Chapter 7 helps students learn similarity rules, properties of triangles, and inequalities. This chapter is very important. To do well, students should read this chapter and practice all kinds of questions. Some of the very important topics covered in this chapter are the Subsequent Occurrence of Triangles, the Hypotenuse Theorem and the Proof of Congruence of SSS, ASA, and SAS. Students would learn all the properties of Triangles, Triangle Inequalities, LHS and RHS congruence criteria, etc.

Quadrilaterals NCERT Class 9 Mathematics Chapter 8

This chapter will help students understand the properties of quadrilaterals and their combinations with triangles. In this chapter, students must also learn methods to prove theorems and formulas.

Areas of Triangles and Parallelograms Chapter 9

This 9 Class Mathematics chapter is very important for understanding the area and how to find the Area of ​​Triangles and Parallelograms. There are three exercises in this chapter, all of which must be practised. Students should practise as many of the examples in this chapter as possible. This chapter contains many theorems, so students should study and practice this chapter properly. Key Findings from the NCERT Solution for 9 Class Mathematics The Area of ​​Parallelograms and Triangles is a very important chapter for coordinate geometry in 9 Class Mathematics. The NCERT solutions to Class 9 Mathematics chapter 9 are primarily focused on themes such as Areas of Parallelograms and Triangles, Triangles and Parallelograms on the Same Base and on the Same Parallel Lines, and Figures on the Same Base and on the Same Parallel Lines. Below are some of the key points from this chapter. Students are encouraged to remember these points, as they will be very useful for getting good scores in the final exam.

• A shape’s area can be defined as a number associated with the portion of the plane enclosed by that shape. Two congruent geometries may have equal areas, but not vice versa.
• Two shapes are on the same base if they share a common base (edge) and the opposite vertex(es) of each shape’s common base lie on a line parallel to the base​​, between the same parallels.
• Parallelograms on the same base (or the same base) and between the same parallels have equal areas.
• Parallelograms with the same base(s) and the same area lie between the same parallels.
• Triangles on the same base(s) and between the same parallels have the same area. Triangles with the same base (or bases) and area are between the same parallels.
• A bisector divides a triangle into two equal triangles.

Class 9 Mathematics Chapter 10

Chapter 10 of Class 9 is an interesting and important chapter for students. Students would learn about Circles, Chords, and Minor Angles, and how to calculate the distance between Chords and the Centre of a Circle. Students will learn the definition of a Circle. They will also need to learn formulas to find the Area of ​​a Circle, Perimeter, etc. There are some theorems and proofs that need to be learned and practised.

Class 9 Mathematics Chapter 11

This is a very important chapter, mainly focused on creating Triangles, Line Bisectors and Measuring Angles such as 45°, 60°, and 90°. This chapter is very important, and the questions in this chapter are considered very important from the examination point of view. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 include topics such as Triangle Construction and Construction of Line Bisectors. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 can be helpful in acquiring a comprehensive understanding of the chapter.

Class 9 Mathematics Chapter 12 Heron’s Formula

In this chapter, students will learn how to find the Area of ​​triangles, of Different Types of Polygons, and of Quadrilaterals using Heron’s Formula. Some of the key subjects to learn and practice are: formulas involved i.e, heron’s formula and exercises which are related to it.

Surface Areas and Volumes Class 9 Mathematics Chapter 13

The themes encapsulated in this chapter were taught to students in previous classes. Therefore, they should pay attention to the theorems and formulas contained in this chapter. Important concepts within this chapter are the formulae of the Volumes of Cubes, Cylinders, Cuboids, Cones, Hemispheres, and Spheres. In this chapter, they will also learn how to transform one figure into another and how to compare the volumes of two figures.

Statistics NCERT Class 9 Mathematics Chapter 14

In this chapter, students will learn about Descriptive Statistics and Data Collection. These concepts help interpret the data and present the results obtained from it. In this chapter, they should learn how to collect, interpret and analyse data. They need to learn how to sort and group data. Topics that they should study and practice for exams include Bar Graphs, Frequency Polygons, and Histograms. They also need to learn about the mathematical concepts of Mean, Mode, and Median. They must solve the practice problems and practice diagrams.

Probability NCERT Class 9 Mathematics Chapter 15

Solving Chapter 15 of Mathematics for Class 9 is important because all the problems contained in this chapter are very interesting and based on everyday life situations. This makes them easier to understand. This chapter is also very important and students should practice it properly.

It is noteworthy that students who study with the aid of NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 for Class 9, will get high marks.

Q.1 Construct an angle of 90° at the initial point of a given ray and justify the construction.

Ans

Given:

A ray OA with initial point O is given.

To construct:

An angle of 90°

Steps of Construction:

(i) Draw a ray OA with initial point O.

(ii) Mark an arc of any radius with centre O.

(iii) Mark two arcs with same radius and centre at the points M1 and M2 respectively.

(iv) Now mark an arc with centre M2 and another arc with centre M3 with any radius. These arcs intersect at N.

(v) Join O and N by a ray OB.

(vi) ∠BOA is required angle of 90°.

Justification:

(i) Since, ∠M2OA = ∠M3OM2 = 60°

(ii) Ray OB is bisector of ∠M3OM2 i.e.

∠BOM2 = (1/2) ∠M3OM2

= (1/2) 60°

= 30°

(iii) ∠BOA = ∠BOM2 + ∠M2OA

= 30° + 60°

= 90°

Hence, it is justified that ∠BOA = 90°.

Q.2 Construct an angle of 45° at the initial point of a given ray and justify the construction.

Ans

Given:

A ray with initial point O is given.

To construct:

An angle of 45°

Steps of Construction:

(i) Draw a ray OA with initial point O.

(ii) Mark an arc of any radius with centre O.

(iii) Mark two arcs with same radius and centre at the points M1 and M2 respectively.

(iv) Now mark an arc with centre M2 and another arc with centre M3 with any radius. These arcs intersect at N.

(v) Join O and N by a ray OB.

(vi) ∠BOA is an angle of 90°.

(vii) Now, mark arcs of any radius with centre M1 and Q respectively, which intersect at P.

(viii) Draw ray OC through P, we get ∠COA which is equal to 45°.

(ix) Thus, ∠COA is required angle.

Justification:

∠COA = (1/2) ∠BOA
= (1/2) 90°
= 45°

Q.3 Construct the angles of the following measurements: (i) 30° (ii) 22.5° (iii) 15°

Ans

(i)

Given:

A ray with initial point O is given.

To construct:

An angle of 30°

Steps of Construction:

(i) Draw a ray OA with initial point O.
(ii) Mark an arc of any radius with centre O, which intersects ray OA at the point M1.
(iii) Mark another arc with centre M1 and same radius, which intersects earlier arc at M2.
(iv) Now, we draw arcs with any radius and centres M1 and M2 respectively. These arcs intersect at N.

(v) Join O and N with the help of ray OB.

(vi) ∠BOA is required angle of 30°.

(ii)

Given:

A ray with initial point O

To construct:

An angle of 22.5°

Steps of Construction:

(i) Draw a ray OA with initial point O.

(ii) Mark an arc of any radius with centre O.

(iii) Mark two arcs with same radius and centre at the points M1 and M2 respectively.

(iv) Now mark an arc with centre M2 and another arc with centre M3 with any radius. These arcs intersect at N.

(v) Join O and N by a ray OB.

(vi) ∠BOA is an angle of 90°.

(vii) Now, mark arcs of any radius with centre M1 and X respectively, which intersect at P.

(viii) Draw ray OC through P, we get ∠COA which is equal to 45°.

(ix) Now we draw bisector of ∠COA and we get ∠DOA, which is equal to 22.5°.

(x) Thus, ∠DOA is required angle.

(iii)

Given:

A ray with initial point O is given.

To construct:

An angle of 15°.

Steps of Construction:

(i) Draw a ray OA with initial point O.

(ii) Mark an arc of any radius with centre O, which intersects ray OA at the point M1.

(iii) Mark another arc with centre M1 and same radius, which intersects earlier arc at M2.

(iv) Now, we draw arcs with any radius and centres M1 and M2 respectively. These arcs intersect at N.

(v) Join O and N with the help of ray OB.

(vi) ∠BOA is angle of 30°.

(vii) Now, draw bisector OC of ∠BOA.

(viii) ∠COA is required angle of 15°.

Q.4 Construct the following angles and verify by measuring them by a protractor:
(i) 75° (ii) 105° (iii) 135°

Ans

(i)

Given:

A ray with initial point O is given.

To construct:

An angle of 75°

Steps of Construction:

(i) Draw ray OP and construct angle of 90°.

(ii) Mark arcs with centre P and R respectively with any radius. These arcs intersect at Q.

(iii) Draw ray OC throw point Q.

(iv) ∠COA is required angle.

(ii)

Given:

A ray with initial point O is given.

To construct:

An angle of 105°

Steps of Construction:

(v) Draw ray OP and construct angle of 90°.

(vi) Mark arcs with centre P and Q respectively with any radius. These arcs intersect at R.

(vii) Draw ray OC throw point R.

(viii) ∠COA is required angle.

(iii)
Given:

A ray with initial point O is given.

To construct:

An angle of 135°

Steps of Construction:

(i) Draw ray OP and construct angle of 90°.

(ii) Mark arcs with centre P and Q respectively with any radius. These arcs intersect at R.

(iii) Draw ray OC throw point R.

(iv) ∠COA is required angle.

Q.5 Construct an equilateral triangle, given its side and justify the construction.

Ans

Given:

A side of triangle is given.

To construct:

An equilateral triangle ABC

Steps of Construction:

(i) Draw a side of given length.

(ii) Draw two arcs of radius AB with centres A and B respectively. These arcs intersect at C.

(iii) Join AC and BC.

(iv) ΔABC is required triangle.

## FAQs (Frequently Asked Questions)

### 1. Why are NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 important?

The NCERT books are the primary source of information available for examination preparation. NCERT textbook exercises and questions for Class 9 are very helpful for assessment. Students should practice the problem-solving techniques provided in NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 by solving problems on a regular basis. Therefore, referring to NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 for credible solutions will give students a proper understanding of the methods used to solve the problem.

### 2. How do students get NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1?

Students can access Extramarks’s NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 if they need help answering the questions provided in the NCERT book. They can access NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 through the Extramarks educational website and Learning App. Also, by referring to these solutions, students will be able to understand mathematical concepts well and do well in exams.

### 3. Where can students find the NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 chapter-by-chapter answers?

The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 are provided by Extramarks and are accessible to students who need help answering the questions provided in the various exercises in the NCERT Class 9 Mathematics book. Students can find step-by-step solutions to all questions and exercises in each chapter of the Class 9 syllabus. The NCERT Solutions For Class 9 Maths Chapter 11 Exercise 11.1 can be procured from the Extramarks learning platform.