# NCERT Solutions for Class 9 Math

## NCERT Solutions for Class 9 Math

If you are facing any kind of problem while solving any questions of the

**NCERT Class 9th Math**Textbook then you can find in this page. Here, we have provided**NCERT Solutions for Class 9 Math**in detail way so that you understand the problem easily and at the same time grasp the concepts behind the question. The**NCERT Solutions of Math**provided on StudyRankers are prepared by our experts that includes every single step of the solutions which will make your task easy. You can view chapterwise solutions clicking on the name of the chapter provided below.- Chapter 1- Number Systems
- Chapter 2- Polynomials (Part-1) upto Exercise 2.3
- Chapter 2- Polynomials (Part-2) from Exercise 2.4
- Chapter 3- Coordinate Geometry
- Chapter 4- Linear Equations in Two Variables
- Chapter 5- Introduction to Euclid's Geometry
- Chapter 6- Lines and Angles
- Chapter 7- Triangles
- Chapter 8- Quadrilaterals
- Chapter 9- Areas of Parallelograms and Triangles (Part-1)
- Chapter 9- Areas of Parallelograms and Triangles (Part-2)
- Chapter 10- Circles
- Chapter 11- Constructions
- Chapter 12- Heron's Formula
- Chapter 13- Surface Areas and Volumes (Part-1)
- Chapter 13- Surface Areas and Volumes (Part-2)
- Chapter 13- Surface Areas and Volumes (Part-3)
- Chapter 14- Statistics
- Chapter 15- Probability

**Chapter 1 - Number System**

In this chapter, we will learn about the two parts of real numbers, rational numbers and irrational numbers. We will learn how to find rational numbers between two rational numbers and decimal representation of rational and irrational numbers. In the previous class, we read to represent number on number line and in this class we will see how to represent terminating/non-terminating recurring decimals on the number line. We will learn another way of representing real numbers on real number line is through process of successive magnification. In this method we successively decrease the lengths of the intervals in which given number lies. We will also learn about the presentation of square roots of 2, 3 and other non-rational numbers. At last we will study about rationalisation and laws of exponents. The process of converting an irrational denominator of a number to a rational number by multiply its numerator and denominator by a suitable number is called rationalisation.

**Chapter 2 - Polynomials**

An algebraic expression, in which the variables involved have only whole number powers, is called a polynomial. Polynomials of degree 1, 2 and 3 are called linear, quadratic and cubic polynomials respectively. Polynomials containing one, two and three non-zero terms are called monomial, binomial and trinomial respectively. In this chapter, we will dealing with the degrees, coefficient, zeroes and terms of a polynomial. We will find zero of polynomial through factor and remainder theorem.

**Chapter 3 - Coordinate Geometry**

he branch of mathematics in which geometric problems are solved using coordinate systems is known as Coordinate Geometry. In this chapter, we are learning about the coordinate plane, axes, abscissa, ordinates, cartesian system, Quadrants etc. The plane is called the cartesian or coordinate plane and the mutually perpendicular lines are called axes. The horizontal line is called the x-axis and the vertical line is called the y-axis. The x-coordinate of a point is called the abscissa. The y-coordinate of a point is called the ordinate. The axes divide the plan in four quadrants. Two number lines mutually perpendicular to each other are called axes. One of them is horizontal and called as x-axis (as shown by XOX' in the following figure). The other line is perpendicular to XOX'. The vertical line YOY', is called y-axis. Both these lines are in the same plane, called the ‘cartesian plane’ or ‘coordinate plane’ or the ‘XY-plane’.

**Chapter 4 - Linear Equations in two Variables**

This chapter is about linear equations in two variables of the type ax + by + c = 0. An equation of the form ax + by + c = 0; where a, b and care real numbers, such that a and b are not both zero, is called a linear equation in two variables. The questions of this chapter is about proving a linear equation has infinite number of solutions, drawing graphs of linear equations and solving some world problems.

**Chapter 5 - Introduction to Euclid's Geometry**

Euclid was a Greek mathematician, who introduced the method of proving a geometrical result by using logical reasonings on previously proved and known results. This chapter is about the Euclid's axioms and postulates. We will know the relationship between axioms, postulates and theorem. Axioms are the basic facts which are taken for granted without proof. Postulates are the basic facts which are taken for granted specific to geometry, without proof. Theorems are statements which can be proved using definitions and axioms.

**Chapter 6 - Lines and Angles**

An angle is formed by two rays originating from the same point. In this chapter, we will learn about complementary, supplementary and adjacent angles. There are various theorems in htis chapter such as If two lines intersect each other, then the vertically opposite angles are equal. The sum of the three angles of a triangle is 180ยบ.

**Chapter 7- Triangles**

Two congruent figures have exactly the same shape and size. If two triangles are congruent, then their corresponding parts are equal. We will study about the five congruence criterion such as SAS, ASA AAS, SSS and RHS. If two sides and included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent. [SAS congruence rule]

If two angles and the included side of one triangle are equal to two angles and included side of the other triangle, then the two triangles are congruent. [ASA congruence rule] If two angles and one side of a triangle are equal to two angles and the corresponding side of the other triangles, then the two triangles are congruent. [AAS congruence rule] If three sides of one triangle are equal to three sides of other triangle, then the two triangles are congruent. [SSS congruence rule] If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

**Chapter 8- Quadrilaterals**

If A, B, C, D are four points in a plane such that no three of them are collinear and the line segments AB, BC, CD and DA do not intersect except at their end points, the figure formed by these four segments is called a quadrilateral. We will solve the questions based on the properties of quadrilaterals through the help of the properties of triangles.

**Chapter 9 - Areas of Parallelograms and Triangles**

Two congruent figures have equal areas. A diagonal of a parallelogram divides it into two triangles of equal area. Parallelograms on the same base (or equal base) and between the same parallels are equal in area. Triangles on the same base (or equal bases) and between the same parallels are equal in area.

**Chapter 10 - Circles**

Circle is the locus of all such points which are equidistant from a fixed point, this point is known as centre while distance of any point from centre defined as radius of circle. We will learn about chords, arcs, locus and other terms related to circles.

**Chapter 11 - Constructions**

**Chapter 12- Heron's Formula**

In this chapter, we will learn to find area of quadrilaterals, triangles and other types of polygons through Heron's formula. For finding area of a quadrilateral we divide it into various triangles. Then we use Heron’s formula to find the area of the triangles.

**Chapter 13 - Surface Areas and Volumes**

In this chapter, we are solving problems based on surface areas and volumes of cube, cuboids, cylinders, cones, spheres and hemispheres.

**Chapter 14 - Statistics**

Statistics is about the collection, presentation, analysis and interpretation of numerical data. In this chapter, we will see the ways to find the measure of central tendency mean and mode and median of ungrouped or raw data.

**Chapter 15 - Probability**

The numerical measure of uncertainty of an action (or activity) is called probability. This chapter deals with the problems where we have to find probability of certain events.