# NCERT Solutions for Class 10 Maths Chapter 6 Triangles

(Last Updated On: September 6, 2023)

Triangles NCERT Solutions for Class 10 Maths Chapter 6: There are total six exercises consisting of 64 problems. The questions are based on Properties of Triangles and 9 important theorems which are important to score well in CBSE Class 10 exam.

Triangle Introduction: In geometry, a triangle is a polygon with three sides that is formed by joining three non-collinear points. Triangles are one of the most fundamental and important shapes in geometry, and they have many applications in the real world, such as in architecture, engineering, and physics.

There are many different ways to classify triangles including their sides and angles. Triangles can be classified as equilateral, isosceles or scalene on the basis of their sides. An equilateral triangle has three sides of equal length, an isosceles triangle has two sides of equal length, and an equilateral triangle has no sides of equal length.

NCERT Solutions for Class 10 Maths Chapter 6 Triangles can also be classified as acute, obtuse or right angled on the basis of their angles. An obtuse triangle has three angles that are less than 90 degrees, an obtuse triangle has one angle that is greater than 90 degrees, and a right triangle has one angle that is exactly 90 degrees.

In addition to their classification, triangles have several important properties, such as the fact that the sum of the angles in a triangle always adds up to 180 degrees, and that the longest side of a triangle is always opposite the largest angle.

## NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.1

NCERT Solutions for Class 10 Maths Chapter 6 Triangles East East 6.1 are part of the NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 6 Triangle Exercise 6.1

 Board CBSE Textbook NCERT Class Class 10 Subject Maths Chapter Chapter 6 Chapter Name Triangles Exercise Ex 6.1 Number of Questions Solved 3 Category NCERT Solutions

### Type of Triangle

There are several types of triangles based on their sides and angles. Let’s discuss them one by one:

1. Equilateral Triangle: An equilateral triangle is a triangle in which all three sides are of equal length. Each angle of an equilateral triangle measures 60 degrees.
2. Isosceles Triangle: An isosceles triangle is a triangle in which two sides are of equal length. The third side is called the base. The angles opposite to the equal sides are equal.
3. Scalene Triangle: A scalene triangle is a triangle in which all three sides are of different lengths. The angles opposite to the different sides are also different.
4. Acute Triangle: An acute triangle is a triangle in which all three angles are less than 90 degrees.
5. Obtuse Triangle: An obtuse triangle is a triangle in which one angle is greater than 90 degrees.
6. Right Triangle: A right triangle is a triangle in which one angle measures exactly 90 degrees. The side opposite to the right angle is called the hypotenuse.
7. Pythagorean Triplets: A set of three integers a, b, and c are said to form a Pythagorean triplet if they satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2. For example, (3,4,5) is a Pythagorean triplet as 3^2 + 4^2 = 5^2.

### Formula to solve the triangle

There are many formulas and theorems that can be used to solve various aspects of a triangle, such as its sides, angles, and area. Here are some of the most commonly used formulas:
1. Pythagorean Theorem: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse.
2. Law of Sines: This formula relates the lengths of the sides and angles of any triangle. It states that a/sin A = b/sin B = c/sin C, where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles.
3. Law of Cosines: This formula can be used to find the length of any side of a triangle when the lengths of the other two sides and the angle opposite the side to be found are known. It states that c^2 = a^2 + b^2 – 2ab cos C, where c is the length of the side to be found, and a, b, and C are the lengths of the other two sides and the angle opposite the side to be found, respectively.
4. Heron’s Formula: This formula can be used to find the area of a triangle given the lengths of its three sides. It states that the area of the triangle, A, is given by A = sqrt(s(s-a)(s-b)(s-c)), where s is half of the perimeter of the triangle, and a, b, and c are the lengths of its sides.

These are just a few of the formulas and theorems used to solve various aspects of a triangle. Depending on the problem, other formulas and techniques may also be used.

## NCERT Solutions for Class 10 Maths Chapter 6 Triangles Ex 6.1 Questions

### Ex 6.1 Class 10 Maths Question 1.

Fill in the blanks by using the correct word given in brackets. (i) All circles are ……………. . (congruent/similar) (ii) All squares are …………… . (similar/congruent) (iii) All …………….. triangles are similar. (isosceles/equilateral) (iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are …………… and (b) their corresponding sides are …………… (equal/proportional)
Solution:

(i) All circles are congruent. (ii) All squares are similar. (iii) All equilateral triangles are similar. (iv) Two polygons of the same number of sides are similar, if (a) their corresponding angles are equal and (b) their corresponding sides are proportional.

### Ex 6.1 Class 10 Maths Question 2.

Give two different examples of pairs of (i) similar figures. (ii) non-similar figures.

(i) Two different examples of pairs of similar figures are:

1. Two equilateral triangles with different side lengths
2. Two circles with different radii.

(ii) Two different examples of pairs of non-similar figures are:

1. A square and a rectangle
2. A triangle and a trapezium.

### Ex 6.1 Class 10 Maths Question 3.

Ex 6.1 Class 10 Maths Question 3.
State whether the following quadrilaterals are similar or not. Solution: ## What are The Triangles

In geometry, a triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the most basic shapes and is used in many mathematical and scientific applications.

Triangles can be classified in various ways, based on their angles or their sides. Here are some of the types of triangles:

1. Equilateral Triangle – A triangle in which all three sides are of equal length.
2. Isosceles Triangle – A triangle in which two sides are of equal length.
3. Scalene Triangle – A triangle in which all three sides are of different lengths.
4. Acute Triangle – A triangle in which all three angles are less than 90 degrees.
5. Obtuse Triangle – A triangle in which one angle is greater than 90 degrees.
6. Right Triangle – A triangle in which one angle measures exactly 90 degrees.
7. Isosceles Right Triangle – A right triangle in which two sides are of equal length.
8. Pythagorean Triplets – A set of three integers a, b, and c are said to form a Pythagorean triplet if they satisfy the Pythagorean theorem, i.e., a^2 + b^2 = c^2.

These are some of the common types of triangles. There are other classifications as well, such as by angles of elevation and depression, by medians and altitudes, etc.

### Use of triangle problems in daily life

Triangles are one of the most important shapes in geometry, and they have many applications in daily life. Here are some examples of how triangles are used in everyday situations:

1. Construction and Architecture: Triangles are used extensively in construction and architecture. For example, architects and builders use right triangles to ensure that corners are square and to calculate measurements for staircases and roofs.
2. Engineering: Engineers use triangles to calculate angles and distances in structures such as bridges and towers.
3. Navigation: Triangles are used in navigation to calculate the distance between two points, using the concept of trigonometry.
4. Sports: Triangles are used in sports such as billiards and bowling to calculate angles and trajectories.
5. Art: Artists use triangles to create perspective in their drawings and paintings.
6. Cooking: Triangles are used in cooking to cut food items into equal portions, such as cutting a pizza into slices.
7. Landscaping: Triangles are used in landscaping to create symmetry and balance in outdoor spaces, such as designing garden beds or pathways.

These are just a few examples of how triangles are used in daily life. Triangles are a fundamental shape that has many practical applications in various fields, making it an important concept to learn in mathematics.

## Faqs About NCERT Solutions for Class 10 Maths Chapter 6 Triangle

### Q: What is a triangle?

A: A triangle is a closed plane figure with three sides and three angles.

### Q: What are the types of triangles based on sides?

A: The types of triangles based on sides are: equilateral, isosceles, and scalene triangles.

### Q: What are the types of triangles based on angles?

A: The types of triangles based on angles are: acute, right, and obtuse triangles.

### Q: What is the Pythagorean Theorem?

A: The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

### Q: What is the area of a triangle?

A: The area of a triangle is equal to half of the product of its base and height, or using Heron’s formula for a triangle with sides a, b, and c: A = sqrt(s(s-a)(s-b)(s-c)), where s is half of the perimeter of the triangle.

### Q: What is the Triangle Inequality Theorem?

A: The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

### Q: What is the Law of Sines?

A: The Law of Sines is a formula that relates the lengths of the sides and angles of any triangle. It states that a/sin A = b/sin B = c/sin C, where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the opposite angles.

### Q: What is the Law of Cosines?

A: The Law of Cosines is a formula that can be used to find the length of any side of a triangle when the lengths of the other two sides and the angle opposite the side to be found are known. It states that c^2 = a^2 + b^2 – 2ab cos C, where c is the length of the side to be found, and a, b, and C are the lengths of the other two sides and the angle opposite the side to be found, respectively.

### Q: What are some real-life applications of triangles?

A: Triangles have many real-life applications, including in construction, architecture, engineering, navigation, sports, art, cooking, and landscaping.

### Q: What is NCERT Solutions for Class 10 Maths Chapter 6 Triangles?

A: NCERT Solutions for Class 10 Maths Chapter 6 Triangles is a set of solutions to the exercises given in the Chapter 6 of the NCERT textbook for Class 10 Mathematics. These solutions have been prepared by subject matter experts in a step-by-step manner to help students understand the concepts and solve problems easily.

### Q: What are the benefits of using NCERT Solutions for Class 10 Maths Chapter 6 Triangles?

A: The benefits of using NCERT Solutions for Class 10 Maths Chapter 6 Triangles are:

• It helps students in understanding the concepts of triangles in a better way.
• It provides step-by-step solutions to all the exercises given in the chapter.
• It helps students in practicing different types of problems related to triangles.
• It helps students in preparing for their exams effectively.
• It saves time and effort of students in finding the solutions to the problems.

### Q: Are the NCERT Solutions for Class 10 Maths Chapter 6 Triangles accurate and reliable?

A: Yes, the NCERT Solutions for Class 10 Maths Chapter 6 Triangles are accurate and reliable. These solutions have been prepared by subject matter experts after extensive research and analysis to provide students with the most accurate and reliable solutions.

### Q: Can NCERT Solutions for Class 10 Maths Chapter 6 Triangles help in improving exam scores?

A: Yes, NCERT Solutions for Class 10 Maths Chapter 6 Triangles can help in improving exam scores. These solutions provide a comprehensive understanding of the concepts and enable students to solve different types of problems related to triangles. With regular practice using these solutions, students can improve their problem-solving skills and prepare well for their exams.

### Q: Can NCERT Solutions for Class 10 Maths Chapter 6 Triangles be used for revision?

A: Yes, NCERT Solutions for Class 10 Maths Chapter 6 Triangles can be used for revision. These solutions provide a quick and easy way to revise the concepts and solve different types of problems related to triangles. By revising using these solutions, students can refresh their memory and prepare themselves for the exams.

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