Explore NCERT Solutions for Class 10 Maths Chapter 3 – Comprehensive Guide

NCERT solutions for class 10 maths chapter 3 cover all important topics with step-by-step explanations. Get detailed answers to enhance your understanding and score better.

Here are some sample questions and answers related to the topic. These have been written to help you understand the concepts better without using typical formulas.

Sample Questions and Answers for Maths Chapter 3:

What is the sum of the interior angles of a triangle?
The sum of the interior angles of any triangle is always 180°.

What is a pair of supplementary angles?
Two angles are supplementary if their sum is 180°. For example, angles of 120° and 60° are supplementary.

What do you mean by complementary angles?
Two angles are complementary if their sum is 90°. For example, if one angle is 45°, the other must be 45° to make 90°.

Can a triangle have two right angles?
No, a triangle cannot have two right angles because the sum of the angles in a triangle must always be 180°.

What is the relationship between the angles in a linear pair?
In a linear pair, the two adjacent angles always add up to 180°.

What are vertically opposite angles?
Vertically opposite angles are the angles formed when two lines intersect. These angles are always equal to each other.

Explain the properties of an isosceles triangle.
An isosceles triangle has two sides of equal length and the angles opposite these sides are also equal.

What is the formula for the area of a triangle?
The area of a triangle is given by half the product of its base and height.

How do you find the perimeter of a triangle?
To find the perimeter of a triangle, you add up the lengths of all three sides.

What is the Pythagorean Theorem?
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

How do you find the height of a triangle if the area and base are known?
You can find the height of the triangle by rearranging the formula for the area of a triangle. Height = (2 × Area) ÷ Base.

What is an equilateral triangle?
An equilateral triangle has all three sides equal in length and all three angles equal, each measuring 60°.

How do you calculate the sum of the exterior angles of a polygon?
The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

What is the difference between a scalene triangle and an isosceles triangle?
A scalene triangle has all sides of different lengths, whereas an isosceles triangle has at least two sides of equal length.

Explain the concept of an obtuse angle.
An obtuse angle is an angle that is greater than 90° but less than 180°.

How do you find the area of a right-angled triangle?
The area of a right-angled triangle is calculated by multiplying the base and the height and dividing the result by 2.

What is a reflex angle?
A reflex angle is an angle that is greater than 180° but less than 360°.

How do you find the length of the hypotenuse in a right triangle?
You can use the Pythagorean theorem to find the length of the hypotenuse. Hypotenuse = √(side1² + side2²).

What is the angle sum property of a quadrilateral?
The sum of all interior angles of a quadrilateral is always 360°.

What is the difference between a parallelogram and a rectangle?
In a parallelogram, opposite sides are parallel, but the angles are not necessarily 90°. In a rectangle, all angles are 90° and opposite sides are parallel.

How do you calculate the perimeter of a rectangle?
To find the perimeter of a rectangle, you add the lengths of all four sides, which is equivalent to 2 × (Length + Width).

What is a rhombus?
A rhombus is a type of parallelogram where all sides are of equal length, but the angles are not necessarily 90°.

How do you calculate the area of a rhombus?
The area of a rhombus can be found by multiplying the lengths of its diagonals and dividing by 2.

What is a square?
A square is a special type of rectangle where all sides are of equal length, and all angles are 90°.

How do you calculate the area of a square?
The area of a square is found by squaring the length of one of its sides (Side × Side).

What are adjacent angles?
Adjacent angles are two angles that share a common vertex and one common arm.

What is the sum of the angles in a quadrilateral?
The sum of the interior angles of any quadrilateral is always 360°.

What do you mean by a right angle?
A right angle is an angle that measures exactly 90°.

What is the angle sum property of a triangle?
The sum of the interior angles of a triangle is always 180°.

How do you find the perimeter of a regular polygon?
The perimeter of a regular polygon is found by multiplying the length of one side by the total number of sides.

What is a convex polygon?
A convex polygon is a polygon in which all the interior angles are less than 180°.

What is the formula for the area of a circle?
The area of a circle is given by the formula πr², where r is the radius of the circle.

What is a sector of a circle?
A sector of a circle is a region enclosed by two radii and the arc between them.

How do you calculate the circumference of a circle?
The circumference of a circle is calculated by multiplying 2π by the radius (C = 2πr).

What is the formula for the area of a sector?
The area of a sector is given by the formula (θ/360) × πr², where θ is the angle of the sector in degrees.

What do you mean by the diameter of a circle?
The diameter of a circle is the straight line passing through the center of the circle, connecting two points on the circumference.

What is a tangent to a circle?
A tangent is a straight line that touches the circle at exactly one point.

What is the difference between a chord and a diameter?
A chord is a line segment joining two points on the circle, whereas the diameter is the longest chord, passing through the center of the circle.

What are concentric circles?
Concentric circles are circles that have the same center but different radii.

What is the formula for the volume of a cylinder?
The volume of a cylinder is calculated by multiplying the area of its base (πr²) by its height (V = πr²h).

How do you find the surface area of a sphere?
The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

What is the volume of a sphere?
The volume of a sphere is given by the formula (4/3)πr³.

What is the surface area of a cone?
The surface area of a cone is given by the formula πr(r + l), where r is the radius and l is the slant height.

What is the volume of a cone?
The volume of a cone is given by the formula (1/3)πr²h, where r is the radius and h is the height.

What is the formula for the area of a trapezium?
The area of a trapezium is given by the formula (1/2) × (sum of parallel sides) × height.

What is the difference between a parallelogram and a rhombus?
A parallelogram has opposite sides equal and parallel, whereas in a rhombus, all sides are equal, but the angles are not necessarily 90°.

What is the formula for the perimeter of a parallelogram?
The perimeter of a parallelogram is calculated as 2 × (Length + Width).

What is the formula for the area of a rectangle?
The area of a rectangle is calculated by multiplying its length by its width.

What is the difference between a regular and irregular polygon?
A regular polygon has all sides and angles equal, whereas an irregular polygon does not have equal sides or angles.

What is the relationship between the radius and diameter of a circle?
The radius of a circle is half of its diameter. Therefore, the diameter is twice the length of the radius.

Recommended Indian Books for NCERT Solutions for Class 10 Maths Chapter 3

"Mathematics for Class 10" by R.D. Sharma
Publisher: Dhanpat Rai Publications
This book provides a comprehensive explanation of topics from Chapter 3 of Class 10 Maths. It includes detailed examples, step-by-step solutions, and a large variety of practice problems to enhance understanding. It focuses on developing problem-solving skills and provides a deep insight into geometric principles.

"Mathematics for Class 10" by M.L. Agarwal
Publisher: Arya Publications
M.L. Agarwal’s book is renowned for its clear explanations and a plethora of practice questions. This book offers numerous solved and unsolved problems that help students develop a strong foundation in Geometry, especially for Chapter 3, which deals with various theorems and properties of triangles.

"NCERT Exemplar Problems - Mathematics Class 10" by NCERT
Publisher: NCERT
The NCERT Exemplar book is designed to test the deeper understanding of the concepts in Class 10 Maths Chapter 3. It provides a variety of application-based questions, including multiple choice, short answer, and long answer questions that require critical thinking.

"Mathematics Class 10" by R.S. Aggarwal
Publisher: S. Chand Publishing
This book includes a range of questions, from basic to advanced, with detailed solutions. The chapter focuses on the properties of triangles, including the angle sum property and Pythagoras Theorem, with ample examples and exercise questions.

"Together with Mathematics Class 10" by K.K. Saini
Publisher: Rachna Sagar
This book provides a systematic approach to learning Maths, with detailed NCERT solutions for Class 10 Chapter 3. It is especially useful for students who are preparing for competitive exams alongside their school syllabus.

"Mathematics for Class 10" by M.S. Chouhan
Publisher: Goyal Brothers Prakashan
Known for its user-friendly approach, M.S. Chouhan’s book includes comprehensive theory sections, followed by questions that progressively increase in difficulty. This helps build conceptual clarity before tackling more complex problems.

"Objective Mathematics for Class 10" by R.D. Sharma
Publisher: Dhanpat Rai Publications
The objective format of the book is excellent for practice. It includes various types of questions like true/false, fill-in-the-blanks, and multiple-choice questions, which cover all aspects of Chapter 3.

"Problems in Mathematics" by L. R. Arora
Publisher: S. Chand Publishing
This book is known for its problem-solving techniques. It is ideal for students who want to master theorems, angles, and properties of triangles. The exercises are challenging and offer a range of practice that tests understanding and application.

"NCERT Solutions for Class 10 Mathematics" by NCERT
Publisher: NCERT
This is the official solutions book and is incredibly useful for students following the NCERT curriculum. It includes detailed solutions for all the questions in Chapter 3, along with explanations and diagrams.

"Mathematics for Class 10" by R.P. Bansal
Publisher: Laxmi Publications
R.P. Bansal’s book is great for preparing for board exams. The chapter content includes thorough explanations on geometry topics, detailed solved examples, and a large variety of practice problems on triangles.

"Mathematics for Class 10" by P.K. Agarwal
Publisher: Vikas Publication
This book is a go-to for practicing exercises related to geometric shapes and their properties. Chapter 3 focuses heavily on triangle properties, offering various approaches and types of questions for in-depth practice.

"Real Life Mathematics for Class 10" by R.K. Bansal
Publisher: Punjab University Press
It combines real-life examples with geometric theorems, providing students with contextual problems from real-world scenarios. The exercises encourage students to think beyond the textbook.

"Class 10 Mathematics" by S. K. Gupta
Publisher: Laxmi Publications
This book is designed to cover the entire syllabus with an emphasis on practical questions. The exercises in Chapter 3 offer a variety of question types, including proofs, properties, and applications.

"A Problem Book in Mathematics" by V. Kumar
Publisher: Arihant Publications
V. Kumar’s book provides an extensive collection of questions, especially focusing on problem-solving strategies for Chapter 3 topics. It helps students prepare effectively for competitive exams and board exams.

"Mathematics: A Comprehensive Approach" by R. B. Pandey
Publisher: A.D. Publishers
This book is known for its conceptual clarity and simple language. It breaks down geometric concepts and theorems of Chapter 3, making it easy for students to grasp and apply the concepts.

"Step by Step Mathematics Class 10" by H.C. Verma
Publisher: Bharti Publications
H.C. Verma’s book is designed for students looking to excel in both school exams and competitive exams. The chapter on triangles is particularly rich in problems that enhance logical thinking and geometric reasoning.

"Mathematics for Class 10" by S.K. Mangal
Publisher: Modern Publishers
The book contains both theoretical content and a vast range of practice problems. It ensures that students grasp the fundamental concepts of Chapter 3 before moving on to advanced problems.

"Comprehensive Mathematics for Class 10" by L. R. Arora
Publisher: S. Chand Publishing
L.R. Arora’s book is comprehensive in nature, with detailed explanations and exercises. The book provides ample practice for theorems and postulates in Chapter 3, covering a wide range of difficulty levels.

"Complete Mathematics for Class 10" by J.B. Gupta
Publisher: VK Publications
This book offers a systematic approach to learning Geometry, with numerous practice exercises, including practical and application-based problems, which enhance students' understanding of Chapter 3 topics.

"Advanced Problems in Mathematics for Class 10" by N. B. Singh
Publisher: Vikas Publications
N.B. Singh’s book is focused on high-level problem-solving skills. It provides challenging questions that encourage deep thinking and application of concepts learned in Chapter 3.

NCERT Solutions for Class 10 Maths Chapter 3: A Comprehensive Guide

Mathematics in Class 10 holds a pivotal role in shaping students' understanding of geometry. Chapter 3, which focuses on the properties of triangles, is a critical chapter in this curriculum. It covers a range of important concepts, including various theorems and properties that are fundamental to understanding the structure of triangles. These concepts are essential not only for academic exams but also for real-world applications in fields like architecture, engineering, and design.

To begin with, the core of Chapter 3 is the study of triangles and their properties. Students delve into understanding the Pythagorean theorem, the properties of equilateral, isosceles, and scalene triangles, and the angle sum property of triangles. These concepts build the foundation for higher mathematical studies and are often tested in board exams. The chapter includes critical theorems such as the basic proportionality theorem, which deals with the relationship between the sides and angles of triangles.

The NCERT solutions for this chapter are designed to provide clarity and enhance problem-solving skills. These solutions guide students through step-by-step processes of solving geometrical problems, making complex topics more accessible. Moreover, the chapter includes a variety of exercises, ranging from simple to complex, that encourage students to apply theorems and properties in different scenarios. This not only prepares students for exams but also improves their logical reasoning abilities.

The content of this chapter is designed to be interactive, with diagrams and illustrations accompanying every concept. Theorems like the angle bisector theorem, which states that the angle bisector of a triangle divides the opposite side in the ratio of the adjacent sides, are explained in simple terms with practical examples. Such explanations enable students to visualize geometric relationships and solve problems efficiently.

Additionally, the chapter provides numerous application-based problems, encouraging students to think critically about how these geometric properties apply to real-world situations. This approach makes learning more engaging and prepares students to apply their knowledge in both academic and practical contexts.

As students work through the NCERT solutions for Class 10 Maths Chapter 3, they gain a deeper understanding of triangles and their properties, ensuring a solid foundation for future mathematical concepts. The diverse range of questions, from basic exercises to advanced problems, prepares students thoroughly for their exams and beyond. The book, with its clear explanations and practical exercises, is an indispensable resource for any student aiming to excel in Mathematics.