NCERT Class 10 Maths Chapter 6: Complete Resource for Triangles
The benefits of using NCERT Solutions for Class 10 Maths Triangles PDF is profound. The PDF of Class 10 Maths Chapter 6 NCERT Solutions has been prepared by expert mathematicians at Vedantu after thorough research on the subject matter. All the solutions provided here are written in a simple and lucid manner. With the aid of these NCERT Solutions for Class 10 Chapter 6 of Maths, students can not only improve their knowledge but also aspire to score better in their examinations.
What is even better is that you can now download these NCERT Solutions for Class 10 Chapter Triangles PDF for free. The PDF will allow you to refer to these solutions as per your need and convenience. Download NCERT Solution PDF today to have easy access to all subject solutions for free which also includes Class 10 Science NCERT Solutions.
Exercises under NCERT Solutions for Class 10 Maths Chapter 6 Triangles
NCERT Solutions for Class 10 Maths Chapter 6, "Triangles," is a chapter that deals with the properties and classification of triangles. The chapter contains six exercises, each covering a different aspect of the topic. Below is a brief explanation of each exercise:
Exercise 6.1: In this exercise, you will be introduced to the basic concepts of triangles, including the definition, elements, types, and angles. You will also learn about congruent triangles and the criteria for their congruence.
Exercise 6.2: This exercise focuses on the properties of triangles, such as the angle sum property, the exterior angle property, and the inequality theorem. You will also learn about the Pythagorean theorem and its applications.
Exercise 6.3: In this exercise, you will learn about the similarity of triangles, including the criteria for similarity, the theorem of basic proportionality, and the application of similarity in practical situations.
Exercise 6.4: This exercise covers the mid-point theorem, which states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length. You will also learn about the converse of this theorem.
Exercise 6.5: In this exercise, you will learn about the altitude and median of a triangle and their properties. You will also learn about the centroid and the orthocenter of a triangle.
Exercise 6.6: This exercise covers the concept of the circumcenter and incenter of a triangle and their properties. You will also learn about the construction of circumcenter and incenter using various methods.
NCERT Maths Class 10 Chapter 6 - Free PDF Download
You can opt for Chapter 6 - Triangles NCERT Solutions for Class 10 Maths PDF for Upcoming Exams and also You can Find the Solutions of All the Maths Chapters below.
NCERT Solutions for Class 10 Maths Other Chapter Solutions PDF Download
NCERT Solutions for Class 10 Maths Chapter 6 Triangles Details
Given below are the details of the various sub-topics included in the Class 10 Chapter 6 Triangles NCERT Solutions:
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.1 Introduction
The PDF of Class 10 Maths Triangles recalls students’ knowledge in this introduction part. Students were already introduced to the concept of Triangles in Class 9 wherein they studied properties such as congruence of Triangles. The introduction part of the chapter basically acts as a window for the students so that they are able to get an insight as to what would they be learning new under the topic of Triangles.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.2 Similar Figures
In this section of the Class 10 Maths Chapter 6, students are introduced to the concept of similar figures. Students are taught the basis of similarity in figures such as squares or equilateral triangles with the same lengths of the sides, circles with the same radii. As the students progress through this topic, they get to understand that similar figures can have the same shape but not necessarily the exact size. The questions from this topic mostly ask students to prove similarity between figures by applying the theorems.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.3 Similarity of Triangles
Once the students are made familiar with the concept of similarity, they are then introduced to the criteria under which two or more triangles are deemed similar. The NCERT Solutions for Class 10 Maths Chapter 6 PDF, in this section, explains the theorem of Basic Proportionality. A thorough understanding of this topic will allow students to form the base for solving complex problems in higher mathematics.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.4 Criteria for Similarity of Triangles
This section outlines and explains the criteria for the similarity of triangles. The basic criteria for two triangles to be called similar include: if their corresponding angles are equal and if the corresponding sides of the triangles are in the same ratio (or proportion). Students will be able to visualise the theorems as they are illustrated with the help of proper examples.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.5 Areas of Similar Triangles
Students can understand the formula and learn the process for finding the surface area of similar triangles in this section. Maths NCERT Class 10 Chapter 6 allows students to find the area of similar triangles with the utilisation of the different theorems.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.6 Pythagoras Theorem
The NCERT Solutions Class 10 Chapter 6 explores the use of the Pythagoras theorem in the case of similar triangles. Students have already learnt the theorem and its proof in Class 9. In this section, students will learn how to prove this theorem by employing the concept of similarity of triangles.
NCERT Solutions for Class 10 Maths Chapter 6 Triangles: 6.7 Summary
The summary comprises all the topics that you have studied in the chapter. Going through the summary will allow you to recollect all that you have learnt in the chapter including the important concepts, theorems, etc.
Points to Remember
1. A triangle is a polygon with three angles and three sides. A triangle's interior angles add up to 180 degrees, whereas its exterior angles add up to 360 degrees.
2. A triangle can be classified into the following types based on its angle and sides.
Scalene Triangle: All the three sides of this triangle have different measures.
Isosceles Triangle: Any two sides of this triangle have equal length.
Equilateral Triangle: All the three sides of this triangle are equal and each angle measures 60 degrees.
Acute Angled Triangle: All the angles measure less than 90 degrees.
Right Angle Triangle: Any one of the 3 angles is equal to 90 degrees.
Obtuse-Angled Triangle: One of the angles is greater than 90 degrees.
3. Centroid of a Triangle
The centroid of a triangle is the point where the medians of its three sides intersect. It will always be within the triangle.
4. Incenter of a Triangle
The incenter of a triangle is defined as the point where the angle bisectors of the three angles intersect. It is the point in the triangle where the circle is inscribed. Drawing a perpendicular from the incenter to any of the triangle's sides gives the radius.
5. Circumcenter of the Triangle
The circumcenter of a triangle is defined as the point where the perpendicular bisectors of its three sides intersect. It isn't necessarily located inside the triangle. For an obtuse triangle, it might be outside the triangle, but for a right-angled triangle, it could be at the midpoint of the hypotenuse.
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It also falls outside the triangle in the case of an obtuse triangle and at the vertex of the triangle in the case of a right-angle triangle, just like the circumcenter.
7. Similarity of Triangles
In triangles, we'll use the same condition that two triangles are similar if their respective angles are the same and their corresponding sides are proportionate.
8. Basic Proportionality Theorem
According to Thales theorem, if a line is drawn parallel to any of the triangle's sides so that the other two sides intersect at a distinct point, the two sides are divided in the same ratio.
9. Converse of Basic Proportionality Theorem
It is the inverse of the basic proportionality theorem, which states that if a straight line divides the two sides of a triangle in the same ratio, that straight line is parallel to the triangle's third side.
Similarity Criteria of Triangles
There are four criteria for determining if two triangles are similar or not. They are as follows:
Side-Side- Side (SSS) Criterion
Angle Angle Angle (AAA) Criterion
Angle-Angle (AA) Criterion
Side-Angle-Side (SAS) Criterion
NCERT Solutions for Class 10 Maths Chapter 6 All Exercises
Vedantu's NCERT Solutions for Class 10 Maths Chapter 6 - Triangles provide a comprehensive and accessible resource for students to grasp the intricacies of triangle geometry. With a diverse range of well-structured exercises and step-by-step explanations, these solutions promote a deeper understanding of key concepts. By incorporating real-life applications, students can appreciate the relevance of triangles in everyday scenarios. Vedantu's expertly crafted solutions foster self-confidence in solving complex problems, bolstering students' problem-solving abilities. The user-friendly platform encourages interactive learning, making the study process engaging and enjoyable. As a reliable aid, Vedantu's NCERT Solutions for Class 10 Maths Chapter 6 empower students to excel in their academics and develop a strong foundation in geometry.
FAQs on NCERT Solutions for Class 10 Maths Chapter 6 - Triangles
1. How Many Exercises are There in NCERT Solutions for Class 10 Maths Chapter 6 Triangles?
The Class 10 Maths NCERT Solutions for the Chapter Triangles contain exercises corresponding to each topic. The chapter contains a total of 6 exercises with a total of 65 questions. The questions include a mix of long and short type questions. Students should attempt to understand all the concepts and theorems given in the chapter and then solve the questions in the exercises. Solving these questions will definitely give the students a competitive edge in the exams.
2. How Many Marks are Allotted to the Class 10 Maths Chapter 6 Triangles in the Board Exam?
The Class 10 Maths Chapter 6 Triangles is a part of a broader unit ‘Geometry’ in the Board exams. The unit of Geometry comprises a total of 15 marks in the Board exams. The Triangles chapter is an important chapter as per the examination point of view and as such is likely to carry around 5-6 marks in the Class 10 Board exams.
3. Which are the Important Topics to Remember Present in CBSE Class 10 Chapter 6 Triangles?
In the CBSE Class 10 Maths Chapter 6, the topic discussed is Triangles. The topics that are important from this chapter are:
Similarity theorems of triangles.
Criteria for triangle similarity.
Area calculation of similar triangles.
Pythagoras theorem and the concept of similar triangles.
Students should make sure that they are thorough with all these topics and should leave no stone unturned to practise as many questions as possible while preparing this topic for the exams.
4. Can the PDF of NCERT Solutions for Class 10 Maths Chapter 6 Triangles be Downloaded for Free?
Yes, at Vedantu you can download the NCERT Solutions for Class 10 Maths Chapter 6 Triangles PDF for absolutely free of cost. The solutions of this chapter have been compiled by some of the best subject experts and provide a clear insight into the various concepts included in the chapter. To download the PDF of the Class 10 Maths Chapter 6, you will just be required to click on the link provided on this page.
You can also choose to take a print out of the PDF and keep it handy for revision purposes. You can also download the Vedantu app n your phone from where you will be able to access the top-notch study material for your Class 10 exam preparation at one go.
5. Do I need to practice all the questions given in the NCERT Solutions Class 10 Maths Triangles?
It is a good idea to practice every question given in the NCERT Solutions for the Class 10 Maths chapter on Triangles. This way you will understand all the topics and concepts clearly and solve all the problems easily. You will also gain confidence about the exam with increased speed and accuracy because the NCERT Solutions provided by Vedantu are curated by subject matter experts. These solutions are therefore guaranteed to help you to clear your concepts easily and effectively for your exam.
6. What are the important topics covered in Class 10 Maths NCERT Solutions Chapter 6?
Chapter 6 of the Class 10 Maths NCERT book deals with Triangles. The most important topics that are covered in this chapter are:
Definition of a triangle
Similarity of two polygons with an equal number of edges
Similarity of triangles
Proving the Pythagorean Theorem
The concepts of Class 10 Maths Chapter 6 may be a bit tricky to understand. Therefore it's a good idea to download and study the NCERT solutions for Class 10 Maths. These solutions are prepared by subject matter experts with decades of experience and will help you to understand all concepts thoroughly and easily.
7. How can I score the best in Class 10 Maths Chapter 6 Triangles?
The following points will help you to score well and get to the best of your potential in Class 10 Maths Chapter 6 Triangles:
Understand the concept of this chapter.
Refer to extra materials like NCERT Solutions of Class 10 Maths Chapter 6 Triangles available at free of cost on the Vedantu app and on the Vedantu website.
Solve model papers.
Maintain a separate notebook for formulas and theorems.
Practice graphs and diagrams.
If you want to score better than all your peers, then your best shot is definitely to download the NCERT Solutions for Class 10 Maths by Vedantu. Vedantu’s NCERT solutions are prepared by the best Maths teachers in India and written in easy to understand language.
8. What are the most important theorems that come in Class 10 Chapter 6 Triangles?
The most important theorems in class 10 Chapter 6 Triangles are:
Angle Bisector Theorem
Inscribed Angle Theorem
To clearly understand the major theorems included in the Class 10 Chapter 6 Triangles, it's best to download the NCERT solutions for Class 10 Maths. These solutions will help you in learning advanced theorems like the ones present in this chapter. This way you can be sure that you will be able to score well in your Class 10 board exams as well.