**NCERT Solutions for Class 9 Maths** includes solutions to all the questions given in the NCERT textbook for Class 9. There are 15 chapters in class 9 maths. These NCERT Solutions for Class 9** **cover all the topics included in the NCERT textbook-like Number System, Coordinate Geometry, Polynomials, Euclid’s Geometry, Quadrilaterals, Triangles, Circles, Constructions, Surface Areas and Volumes, Statistics, Probability, etc.

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Student those who are searching for **NCERT Solutions for Class 9 Maths**, then this the right place where you can find chapter-wise NCERT solutions for class 9. All these solution are curated by our expert teacher group, with the help of these **Solutions of NCERT Books for Class 9 Maths**, students can practise all types of questions from the chapters. It will boost your skill also help them in building a foundation for higher-level classes.

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## NCERT Solutions Class 9 Maths

**Chapter 1 Number System****Chapter 2 Polynomials****Chapter 3 Coordinate Geometry****Chapter 4 Linear Equations in Two Variables****Chapter 5 Introduction to Euclids Geometry****Chapter 6 Lines and Angles****Chapter 7 Triangles****Chapter 8 Quadrilaterals****Chapter 9 Areas of Parallelograms and Triangles****Chapter 10 Circles****Chapter 11 Constructions****Chapter 12 Heron’s Formula****Chapter 13 Surface Areas and Volumes****Chapter 14 Statistics****Chapter 15 Probability**

#### NCERT Solutions Class 9 Maths Chapter 1 Number System

This chapter discusses different topics, including rational numbers and irrational numbers. Students will also be learning the extended version of the number line and how to represent numbers (integers, rational and irrational) on it.

**Important Formulas – **

**Operations on Real Numbers**

√(a/b) = √a/√b

√ab = √a √b

(√a + √b) (√a – √b) = a – b

(a + √b) (a – √b) = a^{2} – b

(√a + √b) (√c + √d) = √ac + √ad + √bc + √bd

(√a + √b)^{2} = a + 2√ab + b

**Laws of Exponents for Real Numbers**

a^{m} . a^{n} = a^{m + n}

(a^{m})^{n} = a^{mn}

a^{m}/a^{n} = a^{m – n}, m > n

a^{m}b^{m} = (ab)^{m}

#### NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

The second chapter of **Class 9 Maths Chapter 2 Polynomials** contain the topic that is related with Polynomials, Polynomial is an expression that consists of variables and coefficients, involving the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Students will also learn polynomial, degrees, coefficient, zeros and terms of a polynomial.

**Important Formulas –**

(x + y)^{2} = x^{2} + 2xy + y^{2}

(x – y)^{2} = x^{2} – 2xy + y^{2}

x^{2} – y^{2} = (x + y) (x – y)

(x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2zx

(x + y)^{3} = x^{3} + y^{3} + 3xy(x + y)

(x – y)^{3} = x^{3} – y^{3} – 3xy(x – y)

x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z) (x^{2} + y^{2} + z^{2} – xy – yz – zx)

Dividend = (Divisor × Quotient) + Remainder

#### NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

In this **Chapter 3 Coordinate Geometry** includes the concepts of the cartesian plane, coordinates of a point in xy – plane, terms, notations associated with the coordinate plane, including the x-axis, y-axis, x- coordinate, y-coordinate, origin, quadrants and more.

#### NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variable

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variable – we learn linear equation in two variables, i.e., ax + by + c = 0. Students will also learn to plot the graph of a linear equation in two variables. These are the important point that must be remember.

**Important Points**

- An equation of the form ax + by + c = 0, where a, b and c are real numbers, such that a and b are not both zero, is called a linear equation in two variables.
- A linear equation in two variables has infinitely many solutions.
- The graph of every linear equation in two variables is a straight line.
- x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis.
- The graph of x = a is a straight line parallel to the y-axis.
- The graph of y = a is a straight line parallel to the x-axis.
- An equation of the type y = mx represents a line passing through the origin.

#### NCERT Solutions for Class 9 Maths Chapter 5 Introduction Euclids Geometry

NCERT Solutions Class 9 Maths Chapter 5 Introduction to Euclids Geometry – We study about Euclid’s approach to geometry and tries to link it with the present-day geometry. Introduction to Euclid’s Geometry provides the students with a method of defining common geometrical shapes and terms.

**Important Axioms and Postulates – **

Some of Euclid’s axioms are:

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part.

(6) Things which are double of the same things are equal to one another.

(7) Things which are halves of the same things are equal to one another.

**Euclid’s Five Postulates**

Postulate 1 – A straight line may be drawn from any one point to any other point.

Postulate 2 – A terminated line can be produced indefinitely.

Postulate 3 – A circle can be drawn with any centre and any radius.

Postulate 4 – All right angles are equal to one another.

Postulate 5 – If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.

#### NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

In this topic we learn basic Geometry primarily focusing on the properties of the angles formed i) when two lines intersect each other and ii) when a line intersects two or more parallel lines at distinct points.

#### NCERT Solutions for Class 9 Maths Chapter 7 Triangles

In this Chapter 7 students will study about the congruence of triangles, rules of congruence, some properties of triangles and the inequalities in triangles in details. All These 5 exercises, in which the students are asked “to-prove” as well as application-level problems.