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

Content Curator

The NCERT Solutions for Class 9 Maths have been provided in this article. Lines are dots spaced together that extend infnitely in two directions. Angles are shapes that form once two rays meet at the endpoint.

Class 9 Maths Chapter 6 Lines and Angles belong to Unit 4 Geometry which has a weightage of 27 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 6 cover the following important concepts:

Angle Sum Property of a Triangle
Lines and Angles
Parallel Lines and a Transversal

Download: NCERT Solutions for Class 9 Mathematics Chapter 6 pdf

NCERT Solutions for Class 9 Mathematics Chapter 6

The Chapter 6 Class 9 Maths are given below:

Important Topics in Class 9 Maths Chapter 6 Lines and Angles

Important Topics in Class 9 Maths Chapter 6 Lines and Angles are elaborated below:

Angle Sum Property of a Triangle

Angle sum property of a triangle claims that the sum of interior angles of a triangle is 180°. It is used to determine the measure of an unknown interior angle when the values of the other angles are known.

Angle Sum Property of a Triangle can be expressed by the following formula:
S = ( n − 2) × 180°

Lines and Angles

A line is a straight one-dimensional shape that extends infinitely in two directions. Angles form when two lines intersect one another. It can be represented by the symbol ∠.

Example: List what happens when two parallel lines are intersected by a transversal?

Solution: Assuming that two parallel lines are intersected by a transversal, the following occurs:

The vertically opposite angles are equal.
The corresponding angles are equal as well.
The alternate exterior and interior angles are equal too.

Parallel Lines and a Transversal

Parallel lines always remain the same distance apart and actually never meet. While, a transversal is any line that intersects two or more lines.

Example: What are some properties of a Transversal?

Solution: Some properties of a transversal are:

Its corresponding angles are always equal.
Its vertically opposite angles are found equal.
Its alternate interior angles are equal too.
Its alternate exterior angles are equal too.

NCERT Solutions for Class 9 Maths Chapter 6 Exercises:

The detailed solutions for all the NCERT Solutions for Lines and Angles under different exercises are:

Also check:

Chapter Related Topics
Pairs of Angles	Parallel Lines and a Transversal	Collinear Points
Vertex	Linear Pair Axiom	Transversal
Corresponding Angles Axiom	Alternate Angles	Properties of Parallel Lines
Angle Formula	Obtuse Angle	Class 9 Maths Chapter 6 Lines and Angles MCQs
Adjacent Angles Vertical	Linear Pair of Angles	Intersecting Lines and Non Intersecting Lines

Also Read:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.
View Solution
2.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.
View Solution
3.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.
View Solution
4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5
View Solution
5.
On the day of her examination, Riya sharpened her pencil from both ends as shown below.

The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.
View Solution
6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number
View Solution

View All

Similar Mathematics Concepts

Angle between two lines: Derivation, Types, Formulae

Angle Formula: Definition, Different Types, Solved Example

Collinear Points: Definition, Formula & Solved Examples

Corresponding Angles Axioms: Definition, Types and Sample Questions

Lines and Angles: Types, Properties and Examples

Acute Angle: Properties & Triangle Inequality Theorem

Exterior Angle Theorem: Properties, Proof & Examples

Lines and Angles MCQs

Right Angle: Types, Parts & Geometric Construction

Construction of Perpendicular Lines: Formula, Method, Sample Questions

Mathematics Preparation Guides

Statistics: Mean, Median, Variance and Cumulative Frequency Curve

Remainder Theorem: Definition, Steps & Examples

Angle Formula: Definition, Different Types, Solved Example

Trapezoids: Isosceles, Scalene Properties, Area, Properties, Examples

Quadrilateral Angle Sum Property: Theorem, Types & Example

Frequency Polygons: Steps, Formula & Examples

Area of Parallelogram: How to Calculate Area of Parallelogram?

Congruence of Triangles: SSS, SAS, ASA & RHS Rules

Quadrilateral Formulas: Types and Properties

Properties of Triangle: Types, Formulas & Examples

Class 9 Maths MCQ: Chapter-wise with Solutions

Properties of Parallel Lines: Transitive & Symmetric Properties

Isosceles triangle: Types, Properties, Angles & Examples

Operations on Rational Numbers:Rules, Properties & Examples

Addition and Subtraction of Integers: Rules & Examples

Scalene Triangle: Types, Formulas, Properties & Examples

Quadrant: Types, Sign Convention & Examples

Rationalize the Denominator: Explanation and Solved Examples

Area of a Kite: Formula, Derivation & Examples

Volume of a Pyramid: Formula and Solved Example

Mathematics NCERT Solutions

Linear Equation in Two Variables: Graph, Elimination and Substitution

Types of Triangles: Important Terms, Scalene, Acute, and Obtuse Triangle

Formula Of Perimeter Shapes

Sphere Formula: Diameter, Surface Area and Volume

Ordinate: Abscissa, Plotting Ordinates, Relation, Solved Examples

Integers as Exponents: Explanation, Rules and Method of Solving

Central Tendency: Definition, Methods and Sample Questions

Line Segment: Definition, Measurement and Examples

Line, Line Segment and Ray: Differentiation and Sample Questions

Area of Equilateral Triangle, Perimeter & Altitude Formulas

You can also check

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

Important Topics in Class 9 Maths Chapter 6 Lines and Angles

Angle Sum Property of a Triangle

Lines and Angles

Parallel Lines and a Transversal

NCERT Solutions for Class 9 Maths Chapter 6 Exercises:

CBSE X Related Questions

1.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

2.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

3.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

Class	15--20	20--25	25--30	30--35	35--40	40--45
Frequency	12	10	15	11	7	5

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

Important Topics in Class 9 Maths Chapter 6 Lines and Angles

Angle Sum Property of a Triangle

Lines and Angles

Parallel Lines and a Transversal

NCERT Solutions for Class 9 Maths Chapter 6 Exercises:

CBSE X Related Questions

1.In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

2.The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

3.Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

4.Find the mean and mode of the following data:Class15--2020--2525--3030--3535--4040--45Frequency1210151175

6.Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that (i) $pqr + 1$ is a composite number (ii) $pqr + 1$ is a prime number

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.

2.
The number of red balls in a bag is three more than the number of black balls. If the probability of drawing a red ball at random from the given bag is $\dfrac{12}{23}$, find the total number of balls in the given bag.

3.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

4.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

6.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number