Class 6 Exam > Class 6 Notes > Mathematics (Maths) Class 6 > RD Sharma Solutions: Triangles (Exercise 12.1)
Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6 PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
Page 2
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
Page 3
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
Page 4
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
(x) Exterior of a triangle – The region which lies outside the triangle is called the exterior of a triangle.
8. In Fig. 12.13, the length (in cm) of each side has been indicated along the side. State for each triangle
whether it is scalene, isosceles or equilateral.
Solution:
(i) It is a scalene triangle having sides of different lengths.
(ii) It is an isosceles triangle having two sides of same length i.e. 5.6 cm.
(iii) It is an equilateral triangle having all sides of same length i.e. 5 cm.
(iv) It is a scalene triangle having sides of different lengths.
(v) It is an isosceles triangle having two sides of same length i.e. 6.2 cm.
9. In Fig. 12.14, there are five triangles. The measures of some of their angles have been indicated. State for
each triangle whether it is acute, right or obtuse.
Solution:
Page 5
1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What
figure do you get? Name the triangle. Also, name
(i) the side opposite to ? B
(ii) the angle opposite to side AB
(iii) the vertex opposite to side BC
(iv) the side opposite to vertex B.
Solution:
Consider A, B and C as three non-collinear points and join them.
By joining the points we obtain a triangle having three sides which is the ? ABC
(i) The side opposite to ? B is AC.
(ii) The angle opposite to side AB is ? ACB.
(iii) The vertex opposite to side BC is A.
(iv) The side opposite to vertex B is AC.
2. Take three collinear points A, B and C on a page of your notebook. Join AB, BC and CA. Is the figure a
triangle? If not, why?
Solution:
Consider A, B and C as three collinear points and join AB, BC and CA.
We get a straight line which has only one side and not a triangle. The straight line is not a closed figure whereas
the triangle is a closed figure which has three sides.
3. Distinguish between a triangle and its triangular region.
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
4. In Fig. 12.11, D is a point on side BC of a ? ABC. AD is joined. Name all the triangles that you can
observe in the figure. How many are they?
Solution:
The triangles which are present in the figure are ? ACD, ? ADB and ? ABC. There are three triangles present in
the given figure.
5. In Fig. 12.12, A, B, C and D are four points, and no three points are collinear. AC and BD intersect at O.
There are eight triangles that you can observe. Name all the triangles.
Solution:
The triangles which are present in the figure are ? ABC, ? ABD, ? ABO, ? BCO, ? DCO, ? AOD, ? ACD and
? BCD. There are about eight triangles which are present in the figure.
6. What is the difference between a triangle and triangular region?
Solution:
The triangle is defined as a plane figure which is formed by three line segments which are non-parallel whereas a
triangular region is the region which is inside a triangle.
The figure given below represents a triangle with a triangular region which is shaded.
7. Explain the following terms:
(i) Triangle
(ii) Parts or elements of a triangle
(iii) Scalene triangle
(iv) Isosceles triangle
(v) Equilateral triangle
(vi) Acute triangle
(vii) Right triangle
(viii) Obtuse triangle
(ix) Interior of a triangle
(x) Exterior of a triangle.
Solution:
(i) Triangle – A plane figure formed by three non-parallel line segments is called a triangle.
(ii) Parts or elements of a triangle – The three sides, three angles and three vertices of a triangles are called parts
or elements of a triangle.
(iii) Scalene triangle – A triangle in which all the sides are different is called a scalene triangle.
(iv) Isosceles triangle – A triangle whose two sides are equal is called an isosceles triangle.
(v) Equilateral triangle – A triangle whose all sides are equal to one another is called an equilateral triangle.
(vi) Acute triangle – A triangle whose all the angles are acute is called acute-angled triangle or an acute triangle.
(vii) Right triangle – A triangle whose one angle is a right angle is called a right-angled triangle or a right triangle.
(viii) Obtuse triangle – A triangle whose one angle is obtuse is called an obtuse-angled triangle or an obtuse
triangle.
(ix) Interior of a triangle – The region which lies inside the triangle is called the interior of a triangle.
(x) Exterior of a triangle – The region which lies outside the triangle is called the exterior of a triangle.
8. In Fig. 12.13, the length (in cm) of each side has been indicated along the side. State for each triangle
whether it is scalene, isosceles or equilateral.
Solution:
(i) It is a scalene triangle having sides of different lengths.
(ii) It is an isosceles triangle having two sides of same length i.e. 5.6 cm.
(iii) It is an equilateral triangle having all sides of same length i.e. 5 cm.
(iv) It is a scalene triangle having sides of different lengths.
(v) It is an isosceles triangle having two sides of same length i.e. 6.2 cm.
9. In Fig. 12.14, there are five triangles. The measures of some of their angles have been indicated. State for
each triangle whether it is acute, right or obtuse.
Solution:
(i) It is a right triangle with one angle as 90
o
.
(ii) It is an obtuse triangle with one angle as 120
o
.
(iii) It is an acute triangle with one angle as 60
o
.
(iv) It is a right triangle with one angle as 90
o
.
(v) It is an obtuse triangle with one angle as 110
o
.
10. Fill in the blanks with the correct word/symbol to make it a true statement:
(i) A triangle has ……. sides.
(ii) A triangle has …….. verticals.
(iii) A triangle has …….. angles.
(iv) A triangle has …….. parts.
(v) A triangle whose no two sides are equal is known as ……..
(vi) A triangle whose two sides are equal is known as ……..
(vii) A triangle whose all the sides are equal is known as …….
(viii) A triangle whose one angle is a right angle is known as ……..
(ix) A triangle whose all the angles are of measures less than 90
o
is known as …….
(x) A triangle whose one angle is more than 90
o
is known as …….
Solution:
(i) A triangle has three sides.
(ii) A triangle has three verticals.
(iii) A triangle has three angles.
(iv) A triangle has six parts.
(v) A triangle whose no two sides are equal is known as scalene.
(vi) A triangle whose two sides are equal is known as isosceles.
(vii) A triangle whose all the sides are equal is known as equilateral.
(viii) A triangle whose one angle is a right angle is known as right triangle.
(ix) A triangle whose all the angles are of measures less than 90
o
is known as acute triangle.
(x) A triangle whose one angle is more than 90
o
is known as obtuse triangle.
11. In each of the following, state if the statement is true (T) or false (F):
(i) A triangle has three sides.
(ii) A triangle may have four vertices.
(iii) Any three line-segments make up a triangle.
(iv) The interior of a triangle includes its vertices.
(v) The triangular region includes the vertices of the corresponding triangle.
(vi) The vertices of a triangle are three collinear points.
Read More
|
94 videos|347 docs|54 tests
|
FAQs on Triangles (Exercise 12.1) RD Sharma Solutions - Mathematics (Maths) Class 6
| 1. How to find the area of a triangle? |  |
Ans. To find the area of a triangle, multiply the length of the base by the height and divide the result by 2. The formula for the area of a triangle is A = (base * height) / 2.
| 2. What is the Pythagorean theorem and how is it used in triangles? | |
Ans. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. It is often used to find the length of one side of a right-angled triangle when the lengths of the other two sides are known.
| 3. How do we classify triangles based on their angles? | |
Ans. Triangles can be classified based on their angles as follows:
- Acute triangle: All angles are less than 90 degrees.
- Obtuse triangle: One angle is greater than 90 degrees.
- Right triangle: One angle is exactly 90 degrees.
| 4. What is the difference between an equilateral triangle and an isosceles triangle? | |
Ans. An equilateral triangle has all three sides and angles equal in length and measure, while an isosceles triangle has two sides and angles equal in length and measure.
| 5. How can we determine if two triangles are similar? | |
Ans. Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. This means that the ratio of the lengths of corresponding sides in the two triangles will be the same.
Related Exams
About this Document
|
4.79/5 Rating |
|
Oct 24, 2024 Last updated |
Document Description: RD Sharma Solutions: Triangles (Exercise 12.1) for Class 6 2024 is part of Mathematics (Maths) Class 6 preparation.
The notes and questions for RD Sharma Solutions: Triangles (Exercise 12.1) have been prepared according to the Class 6 exam syllabus. Information about RD Sharma Solutions: Triangles (Exercise 12.1) covers topics
like and RD Sharma Solutions: Triangles (Exercise 12.1) Example, for Class 6 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Triangles (Exercise 12.1).
Introduction of RD Sharma Solutions: Triangles (Exercise 12.1) in English is available as part of our Mathematics (Maths) Class 6
for Class 6 & RD Sharma Solutions: Triangles (Exercise 12.1) in Hindi for Mathematics (Maths) Class 6 course.
Download more important topics related with notes, lectures and mock test series for Class 6
Exam by signing up for free. Class 6: Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6
Description
Full syllabus notes, lecture & questions for Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6 - Class 6 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 6 | Best notes, free PDF download
Information about RD Sharma Solutions: Triangles (Exercise 12.1)
In this doc you can find the meaning of RD Sharma Solutions: Triangles (Exercise 12.1) defined & explained in the simplest way possible. Besides explaining types of
RD Sharma Solutions: Triangles (Exercise 12.1) theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Triangles (Exercise 12.1) tests, examples and also practice Class 6
tests
|
Explore Courses for Class 6 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Viva Questions
,mock tests for examination
,study material
,Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6
,Extra Questions
,past year papers
,Sample Paper
,Summary
,Semester Notes
,Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6
,Important questions
,practice quizzes
,MCQs
,Objective type Questions
,Previous Year Questions with Solutions
,video lectures
,ppt
,shortcuts and tricks
,Exam
,Triangles (Exercise 12.1) RD Sharma Solutions | Mathematics (Maths) Class 6
,Free
;
Additional Information about RD Sharma Solutions: Triangles (Exercise 12.1) for Class 6 Preparation
RD Sharma Solutions: Triangles (Exercise 12.1) Free PDF Download
The RD Sharma Solutions: Triangles (Exercise 12.1) 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 RD Sharma Solutions: Triangles (Exercise 12.1) now and kickstart your journey towards success in the Class 6 exam.
Importance of RD Sharma Solutions: Triangles (Exercise 12.1)
The importance of RD Sharma Solutions: Triangles (Exercise 12.1) 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.
RD Sharma Solutions: Triangles (Exercise 12.1) Notes
RD Sharma Solutions: Triangles (Exercise 12.1) Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RD Sharma Solutions: Triangles (Exercise 12.1).
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, RD Sharma Solutions: Triangles (Exercise 12.1) Notes on EduRev are your ultimate resource for success.
RD Sharma Solutions: Triangles (Exercise 12.1) Class 6 Questions
The "RD Sharma Solutions: Triangles (Exercise 12.1) 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 RD Sharma Solutions: Triangles (Exercise 12.1) on the App
Students of Class 6 can study RD Sharma Solutions: Triangles (Exercise 12.1) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Triangles (Exercise 12.1),
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 RD Sharma Solutions: Triangles (Exercise 12.1) is prepared as per the latest Class 6 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup