Open App

Class 6 Exam > Class 6 Notes > Mathematics Class 6 ICSE > Selina Textbook Solutions: Triangles

Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


IMPORTANT POINTS 
1. Collinear Points: Three or more points which lie on the same straight line, are called 
collinear points. 
2. Non-Collinear Points: Three or more points which do not lie on the same line, are 
called non- col linear points. 
3. Triangle: By joining the three non-collinear points, a triangle is formed or A triangle is 
a figure which is enclosed by three lines segments. In the figure, ABC is a triangle. 
4. Parts of triangle: A triangle has six parts, three sides and three angles which are on 
the vertices of the triangle. 
5. Sum of angles of a triangle: The sum of the three angles of a triangle is 180°. 
 
6. Exterior angle of a triangle: If one side of a triangle is produced then the exterior 
angle is formed. Exterior angle of a triangle is equal to sum of its interior opposite 
angles. In other words, we can say that exterior angle of a triangle is greater than each 
of its interior opposite angles. In the figure. 
?ACE is exterior angle and ?ACE = ?A + ?B and also ?ACE > ?A and ?ACF > ?B. 
 
7. Classification of triangles : 
(A) According to their sides. 
(i) Equilateral Triangle: If three sides of a triangle are equal, it is called an equilateral 
triangle. 
(ii) Isosceles Triangle: If any two sides of a triangle are equal, then it is called an 
isosceles triangle. 
(iii) Scalene Triangle: If no two sides of the triangle are equal. Then it is called a 
scalene triangle. 
Page 2


IMPORTANT POINTS 
1. Collinear Points: Three or more points which lie on the same straight line, are called 
collinear points. 
2. Non-Collinear Points: Three or more points which do not lie on the same line, are 
called non- col linear points. 
3. Triangle: By joining the three non-collinear points, a triangle is formed or A triangle is 
a figure which is enclosed by three lines segments. In the figure, ABC is a triangle. 
4. Parts of triangle: A triangle has six parts, three sides and three angles which are on 
the vertices of the triangle. 
5. Sum of angles of a triangle: The sum of the three angles of a triangle is 180°. 
 
6. Exterior angle of a triangle: If one side of a triangle is produced then the exterior 
angle is formed. Exterior angle of a triangle is equal to sum of its interior opposite 
angles. In other words, we can say that exterior angle of a triangle is greater than each 
of its interior opposite angles. In the figure. 
?ACE is exterior angle and ?ACE = ?A + ?B and also ?ACE > ?A and ?ACF > ?B. 
 
7. Classification of triangles : 
(A) According to their sides. 
(i) Equilateral Triangle: If three sides of a triangle are equal, it is called an equilateral 
triangle. 
(ii) Isosceles Triangle: If any two sides of a triangle are equal, then it is called an 
isosceles triangle. 
(iii) Scalene Triangle: If no two sides of the triangle are equal. Then it is called a 
scalene triangle. 
 
(B) According to Angles : 
(i) Acute-angled Triangle: A triangle whose each angle is acute, is called an acute 
angled triangle. 
(ii) Right-angled Triangle: A triangle whose one angle is a right angle i.e. 90°, is called 
a right angled triangle. 
(iii) Obtused-angled Triangle: A triangle whose one angle is an obtused angle, is 
called an obtused-angled triangle. 
 
8. Some special properties of a triangle: 
(i) If one angle of a triangle is equal to the sum of other two cycles, the angle is a right 
angled. 
(ii) If the acute angles of a right angled triangle are equal, then the triangle is a right 
angled isosceles triangle and its each acute angle will be of 45°. 
(iii) Sum of two sides of a triangle is greater than the third side. 
(iv) There can be only one right angle in a triangle. 
(v) There can be only one obtuse angle in a triangle. 
(vi) Side opposite to greater angle is greater. 
(vii) Angle opposite to shorter side is shorter. 
EXERCISE 26 (A) 
Question 1. 
In each of the following, find the marked unknown angles : 
Page 3


IMPORTANT POINTS 
1. Collinear Points: Three or more points which lie on the same straight line, are called 
collinear points. 
2. Non-Collinear Points: Three or more points which do not lie on the same line, are 
called non- col linear points. 
3. Triangle: By joining the three non-collinear points, a triangle is formed or A triangle is 
a figure which is enclosed by three lines segments. In the figure, ABC is a triangle. 
4. Parts of triangle: A triangle has six parts, three sides and three angles which are on 
the vertices of the triangle. 
5. Sum of angles of a triangle: The sum of the three angles of a triangle is 180°. 
 
6. Exterior angle of a triangle: If one side of a triangle is produced then the exterior 
angle is formed. Exterior angle of a triangle is equal to sum of its interior opposite 
angles. In other words, we can say that exterior angle of a triangle is greater than each 
of its interior opposite angles. In the figure. 
?ACE is exterior angle and ?ACE = ?A + ?B and also ?ACE > ?A and ?ACF > ?B. 
 
7. Classification of triangles : 
(A) According to their sides. 
(i) Equilateral Triangle: If three sides of a triangle are equal, it is called an equilateral 
triangle. 
(ii) Isosceles Triangle: If any two sides of a triangle are equal, then it is called an 
isosceles triangle. 
(iii) Scalene Triangle: If no two sides of the triangle are equal. Then it is called a 
scalene triangle. 
 
(B) According to Angles : 
(i) Acute-angled Triangle: A triangle whose each angle is acute, is called an acute 
angled triangle. 
(ii) Right-angled Triangle: A triangle whose one angle is a right angle i.e. 90°, is called 
a right angled triangle. 
(iii) Obtused-angled Triangle: A triangle whose one angle is an obtused angle, is 
called an obtused-angled triangle. 
 
8. Some special properties of a triangle: 
(i) If one angle of a triangle is equal to the sum of other two cycles, the angle is a right 
angled. 
(ii) If the acute angles of a right angled triangle are equal, then the triangle is a right 
angled isosceles triangle and its each acute angle will be of 45°. 
(iii) Sum of two sides of a triangle is greater than the third side. 
(iv) There can be only one right angle in a triangle. 
(v) There can be only one obtuse angle in a triangle. 
(vi) Side opposite to greater angle is greater. 
(vii) Angle opposite to shorter side is shorter. 
EXERCISE 26 (A) 
Question 1. 
In each of the following, find the marked unknown angles : 
 
 
Solution: 
(i) Since, sum of all angles of triangle = 180° 
Hence, 70° + 72° + z = 180° 
? 142°+ z = 180° ” 
? z= 180°-142° 
z = 38° 
(ii) Since, sum of all angles of a triangle = 180° 
1st Triangle 50° + 80° + b = 180° 
? 130°+ &= 180° 
?b= 180° – 130° 
b = 50° 
IInd Triangle 40° + 45° + a = 180° 
? 85° + a = 180° 
? a = 180° -85 
a = 95° 
(iii) 60° + 45° + 20° + x = 180° 
? 125° + x = 180° 
? x = 180° – 125° => x = 55° 
Question 2. 
Can a triangle together have the following angles ? 
(i) 55°, 55° and 80° 
(ii) 33°, 74° and 73° 
(iii) 85°, 95° and 22°. 
Solution: 
(i) Sum of all angles of a triangle = 180° Here, 55° + 55° + 80° = 180° 
Page 4


IMPORTANT POINTS 
1. Collinear Points: Three or more points which lie on the same straight line, are called 
collinear points. 
2. Non-Collinear Points: Three or more points which do not lie on the same line, are 
called non- col linear points. 
3. Triangle: By joining the three non-collinear points, a triangle is formed or A triangle is 
a figure which is enclosed by three lines segments. In the figure, ABC is a triangle. 
4. Parts of triangle: A triangle has six parts, three sides and three angles which are on 
the vertices of the triangle. 
5. Sum of angles of a triangle: The sum of the three angles of a triangle is 180°. 
 
6. Exterior angle of a triangle: If one side of a triangle is produced then the exterior 
angle is formed. Exterior angle of a triangle is equal to sum of its interior opposite 
angles. In other words, we can say that exterior angle of a triangle is greater than each 
of its interior opposite angles. In the figure. 
?ACE is exterior angle and ?ACE = ?A + ?B and also ?ACE > ?A and ?ACF > ?B. 
 
7. Classification of triangles : 
(A) According to their sides. 
(i) Equilateral Triangle: If three sides of a triangle are equal, it is called an equilateral 
triangle. 
(ii) Isosceles Triangle: If any two sides of a triangle are equal, then it is called an 
isosceles triangle. 
(iii) Scalene Triangle: If no two sides of the triangle are equal. Then it is called a 
scalene triangle. 
 
(B) According to Angles : 
(i) Acute-angled Triangle: A triangle whose each angle is acute, is called an acute 
angled triangle. 
(ii) Right-angled Triangle: A triangle whose one angle is a right angle i.e. 90°, is called 
a right angled triangle. 
(iii) Obtused-angled Triangle: A triangle whose one angle is an obtused angle, is 
called an obtused-angled triangle. 
 
8. Some special properties of a triangle: 
(i) If one angle of a triangle is equal to the sum of other two cycles, the angle is a right 
angled. 
(ii) If the acute angles of a right angled triangle are equal, then the triangle is a right 
angled isosceles triangle and its each acute angle will be of 45°. 
(iii) Sum of two sides of a triangle is greater than the third side. 
(iv) There can be only one right angle in a triangle. 
(v) There can be only one obtuse angle in a triangle. 
(vi) Side opposite to greater angle is greater. 
(vii) Angle opposite to shorter side is shorter. 
EXERCISE 26 (A) 
Question 1. 
In each of the following, find the marked unknown angles : 
 
 
Solution: 
(i) Since, sum of all angles of triangle = 180° 
Hence, 70° + 72° + z = 180° 
? 142°+ z = 180° ” 
? z= 180°-142° 
z = 38° 
(ii) Since, sum of all angles of a triangle = 180° 
1st Triangle 50° + 80° + b = 180° 
? 130°+ &= 180° 
?b= 180° – 130° 
b = 50° 
IInd Triangle 40° + 45° + a = 180° 
? 85° + a = 180° 
? a = 180° -85 
a = 95° 
(iii) 60° + 45° + 20° + x = 180° 
? 125° + x = 180° 
? x = 180° – 125° => x = 55° 
Question 2. 
Can a triangle together have the following angles ? 
(i) 55°, 55° and 80° 
(ii) 33°, 74° and 73° 
(iii) 85°, 95° and 22°. 
Solution: 
(i) Sum of all angles of a triangle = 180° Here, 55° + 55° + 80° = 180° 
190° ? 180° 
No. 
(ii) 33°+ 74°+ 73°= 180° 
180°= 180° 
Yes. 
(iii) 85° + 95° + 22° = 180° 
202° ? 180° 
No. 
Question 3. 
Find x, if the angles of a triangle are: 
(i) x°, x°, x° 
(ii) x°, 2x°, 2x° 
(iii) 2x°, 4x°, 6x° 
Solution: 
(i) Since, sum of all the angles of a triangle =180 
x° + x° + x° = 180 
? 3x° = 180 
? x° =  
x = 60 
(ii) x° + 2x° + 2x° = 180 
5x° = 180 
x° =  
x° = 36 
(iii) 2x° + 4x° + 6x° =180 
12x° = 180 
x° =  
x° = 15 
Question 4. 
One angle of a right-angled triangle is 70°. Find the other acute angle. 
Solution: 
We know that, sum of angles of a triangle = 180°. 
Let, the acute angle be ‘x’ 
? x + 90° + 70° = 180° 
? x+ 160° = 180° 
? x= 180°-160° 
? x = 20° 
?The acute angle is 20°. 
Question 5. 
In ?ABC, ?A = ?B = 62° ; find ?C. 
Solution: 
?A + ?B + ?C= 180° 
Page 5


IMPORTANT POINTS 
1. Collinear Points: Three or more points which lie on the same straight line, are called 
collinear points. 
2. Non-Collinear Points: Three or more points which do not lie on the same line, are 
called non- col linear points. 
3. Triangle: By joining the three non-collinear points, a triangle is formed or A triangle is 
a figure which is enclosed by three lines segments. In the figure, ABC is a triangle. 
4. Parts of triangle: A triangle has six parts, three sides and three angles which are on 
the vertices of the triangle. 
5. Sum of angles of a triangle: The sum of the three angles of a triangle is 180°. 
 
6. Exterior angle of a triangle: If one side of a triangle is produced then the exterior 
angle is formed. Exterior angle of a triangle is equal to sum of its interior opposite 
angles. In other words, we can say that exterior angle of a triangle is greater than each 
of its interior opposite angles. In the figure. 
?ACE is exterior angle and ?ACE = ?A + ?B and also ?ACE > ?A and ?ACF > ?B. 
 
7. Classification of triangles : 
(A) According to their sides. 
(i) Equilateral Triangle: If three sides of a triangle are equal, it is called an equilateral 
triangle. 
(ii) Isosceles Triangle: If any two sides of a triangle are equal, then it is called an 
isosceles triangle. 
(iii) Scalene Triangle: If no two sides of the triangle are equal. Then it is called a 
scalene triangle. 
 
(B) According to Angles : 
(i) Acute-angled Triangle: A triangle whose each angle is acute, is called an acute 
angled triangle. 
(ii) Right-angled Triangle: A triangle whose one angle is a right angle i.e. 90°, is called 
a right angled triangle. 
(iii) Obtused-angled Triangle: A triangle whose one angle is an obtused angle, is 
called an obtused-angled triangle. 
 
8. Some special properties of a triangle: 
(i) If one angle of a triangle is equal to the sum of other two cycles, the angle is a right 
angled. 
(ii) If the acute angles of a right angled triangle are equal, then the triangle is a right 
angled isosceles triangle and its each acute angle will be of 45°. 
(iii) Sum of two sides of a triangle is greater than the third side. 
(iv) There can be only one right angle in a triangle. 
(v) There can be only one obtuse angle in a triangle. 
(vi) Side opposite to greater angle is greater. 
(vii) Angle opposite to shorter side is shorter. 
EXERCISE 26 (A) 
Question 1. 
In each of the following, find the marked unknown angles : 
 
 
Solution: 
(i) Since, sum of all angles of triangle = 180° 
Hence, 70° + 72° + z = 180° 
? 142°+ z = 180° ” 
? z= 180°-142° 
z = 38° 
(ii) Since, sum of all angles of a triangle = 180° 
1st Triangle 50° + 80° + b = 180° 
? 130°+ &= 180° 
?b= 180° – 130° 
b = 50° 
IInd Triangle 40° + 45° + a = 180° 
? 85° + a = 180° 
? a = 180° -85 
a = 95° 
(iii) 60° + 45° + 20° + x = 180° 
? 125° + x = 180° 
? x = 180° – 125° => x = 55° 
Question 2. 
Can a triangle together have the following angles ? 
(i) 55°, 55° and 80° 
(ii) 33°, 74° and 73° 
(iii) 85°, 95° and 22°. 
Solution: 
(i) Sum of all angles of a triangle = 180° Here, 55° + 55° + 80° = 180° 
190° ? 180° 
No. 
(ii) 33°+ 74°+ 73°= 180° 
180°= 180° 
Yes. 
(iii) 85° + 95° + 22° = 180° 
202° ? 180° 
No. 
Question 3. 
Find x, if the angles of a triangle are: 
(i) x°, x°, x° 
(ii) x°, 2x°, 2x° 
(iii) 2x°, 4x°, 6x° 
Solution: 
(i) Since, sum of all the angles of a triangle =180 
x° + x° + x° = 180 
? 3x° = 180 
? x° =  
x = 60 
(ii) x° + 2x° + 2x° = 180 
5x° = 180 
x° =  
x° = 36 
(iii) 2x° + 4x° + 6x° =180 
12x° = 180 
x° =  
x° = 15 
Question 4. 
One angle of a right-angled triangle is 70°. Find the other acute angle. 
Solution: 
We know that, sum of angles of a triangle = 180°. 
Let, the acute angle be ‘x’ 
? x + 90° + 70° = 180° 
? x+ 160° = 180° 
? x= 180°-160° 
? x = 20° 
?The acute angle is 20°. 
Question 5. 
In ?ABC, ?A = ?B = 62° ; find ?C. 
Solution: 
?A + ?B + ?C= 180° 
? 62° + 62° + ?C = 180° 
? 124° + ?C = 180° 
? ?C = 180° – 124° 
??C = 56° 
Question 6. 
In ?ABC, C = 56°C = 56° ?B = ?C and ?A = 100° ; find ?B. 
Solution: 
?A + ?B + ?C = 180° 
? 100° + ?B + ?B = 180° 
? 2 ?B = 180° 100° 
?B = ° 
?B = 40° 
?C = ?B = 40° 
Question 7. 
Find, giving reasons, the unknown marked angles, in each triangle drawn below: 
 
 
Solution: 
We know that, 
Exterior angle of a triangle is always equal to the sum of its two interior opposite angles

	Mathematics Class 6 ICSE 44 videos\|201 docs\|24 tests

Mathematics Class 6 ICSE

44 videos|201 docs|24 tests

Join Course for Free

About this Document

Oct 02, 2025 Last updated

Related Exams

Class 6

Document Description: Selina Textbook Solutions: Triangles for Class 6 2025 is part of Mathematics Class 6 ICSE preparation. The notes and questions for Selina Textbook Solutions: Triangles have been prepared according to the Class 6 exam syllabus. Information about Selina Textbook Solutions: Triangles covers topics like and Selina Textbook Solutions: Triangles Example, for Class 6 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Selina Textbook Solutions: Triangles.

Introduction of Selina Textbook Solutions: Triangles in English is available as part of our Mathematics Class 6 ICSE for Class 6 & Selina Textbook Solutions: Triangles in Hindi for Mathematics Class 6 ICSE course. Download more important topics related with notes, lectures and mock test series for Class 6 Exam by signing up for free. Class 6: Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE

Description

Full syllabus notes, lecture & questions for Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE - Class 6 | Plus excerises question with solution to help you revise complete syllabus for Mathematics Class 6 ICSE | Best notes, free PDF download

Information about Selina Textbook Solutions: Triangles

In this doc you can find the meaning of Selina Textbook Solutions: Triangles defined & explained in the simplest way possible. Besides explaining types of Selina Textbook Solutions: Triangles theory, EduRev gives you an ample number of questions to practice Selina Textbook Solutions: Triangles tests, examples and also practice Class 6 tests

	Mathematics Class 6 ICSE 44 videos\|201 docs\|24 tests

Mathematics Class 6 ICSE

44 videos|201 docs|24 tests

Join Course for Free

Download as PDF

Explore Courses for Class 6 exam

study material

Summary

pdf

Objective type Questions

Semester Notes

Previous Year Questions with Solutions

practice quizzes

mock tests for examination

ppt

Free

Sample Paper

Exam

Viva Questions

shortcuts and tricks

video lectures

past year papers

Important questions

Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE

MCQs

Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE

Extra Questions

Selina Textbook Solutions: Triangles | Mathematics Class 6 ICSE

;

Additional Information about Selina Textbook Solutions: Triangles for Class 6 Preparation

Selina Textbook Solutions: Triangles Free PDF Download

The Selina Textbook Solutions: Triangles is an invaluable resource that delves deep into the core of the Class 6 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the Selina Textbook Solutions: Triangles now and kickstart your journey towards success in the Class 6 exam.

Importance of Selina Textbook Solutions: Triangles

The importance of Selina Textbook Solutions: Triangles cannot be overstated, especially for Class 6 aspirants. This document holds the key to success in the Class 6 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

Selina Textbook Solutions: Triangles Notes

Selina Textbook Solutions: Triangles Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Selina Textbook Solutions: Triangles. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, Selina Textbook Solutions: Triangles Notes on EduRev are your ultimate resource for success.

Selina Textbook Solutions: Triangles Class 6 Questions

The "Selina Textbook Solutions: Triangles Class 6 Questions" guide is a valuable resource for all aspiring students preparing for the Class 6 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study Selina Textbook Solutions: Triangles on the App

Students of Class 6 can study Selina Textbook Solutions: Triangles alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Selina Textbook Solutions: Triangles, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of Selina Textbook Solutions: Triangles is prepared as per the latest Class 6 syllabus.

Education Revolution