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

• Chapter 1 - Real Numbers

• Chapter 2 - Polynomials

• Chapter 3 - Pair of Linear Equations in Two Variables

• Chapter 4 - Quadratic Equations

• Chapter 5 - Arithmetic Progressions

• Chapter 7 - Coordinate Geometry

• Chapter 8 - Introduction to Trigonometry

• Chapter 9 - Some Applications of Trigonometry

• Chapter 10 - Circles

• Chapter 11 - Constructions

• Chapter 12 - Areas Related to Circles

• Chapter 13 - Surface Areas and Volumes

• Chapter 14 - Statistics

• Chapter 15 - Probability

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.

6. Orthocenter

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

Benefits of Chapter 6 Maths Class 10 NCERT Solutions

There are several benefits of referring to the NCERT Chapter 6 Class 10 Solutions. Students using these solutions to prepare for the exam benefit due to the following reasons:

• The PDF of the Class 10 Maths Chapter Triangles is available for free on the website of Vedantu.

• The solutions have been provided by experts making them reliable and free of errors.

• Students can learn and understand by using these solutions at their convenience with the help of physical copy.

• Students are able to get a good command over the subject which helps them to improve their scores as well.

Conclusion

The solutions of NCERT Class 10 Maths Chapter 6 is a highly reliable source material for students preparing for their exams. Using these solutions can yield many benefits for the students as they can refer to them if they are stuck with a problem or are having trouble gaining command over any topic. Moreover, all the solutions have been provided in a systematic manner so that students are able to make judicious use of their time as they prepare for the exams.

Other Related Links for CBSE Class 10 Maths Chapter 6

• Important Questions for CBSE Class 10 Maths Chapter 6 - Triangles

• Revision Notes for CBSE Class 10 Maths Chapter 6 - Triangles

• Important formulas for CBSE Class 10 Maths Chapter 6 - Triangles