Triangles Class 10 PDF Free Download

Triangles Class 10 PDF Download Info

Triangles Class 10 PDF Free Download, NCERT Solutions for Class 10 Maths Chapter 6 Triangles, notes, mcq, solutions, ncert, solutions pdf, teachoo.

Triangles Class 10 PDF Free Download

From Your Prior Studies, You Are Already Aware With Several Techniques For Determining The Perimeters And Areas Of Basic Plane Shapes Such Rectangles, Squares, Parallelograms, Triangles, And Circles. The Round Shape Is Connected To A Wide Variety Of Everyday Things In One Way Or Another.

Examples Of Such Items Are Bicycle Wheels, A Wheelbarrow (Thela), A Dartboard, A Round Cake, Papad, A Drain Cover, Different Patterns, Bangles, Brooches, Circular Walkways, Washers, Flower Beds, Etc (See Fig. 12.1).

So, The Issue Of Identifying The Perimeters And Regions Of Circular Figures Has Significant Practical Significance.

We Will Study The Perimeter (Circumference) And Area Of A Circle In This Chapter And Then Use That Information To Calculate The Areas Of Two Distinct “Sections” Of A Circular Region—or, More Succinctly, Of A Circle—referred To As The Sector And Segment. Also, We’ll Look At How To Calculate The Areas Of A Few Combinations Of Planar Figures That Include Circles Or Fragments Of Them.

Remember That A Circle’s Perimeter, Also Known As Its Circumference, Is The Distance Travelled After Going Around It Once. Also, You Are Aware From Your Prior Studies That A Circle’s Diameter And Circumference Have A Fixed Relationship.

This page offers NCERT Answers for Class 10 Mathematics Chapter 6 Triangles, which is regarded as one of the most crucial study resources for CBSE Class 10 students. The CBSE Syllabus for 2022–2023 is well-aligned with Chapter 6 of NCERT Solutions for Class 10 Math. It covers a broad subject and presents several rules and theorems. While attempting to answer a range of issues, students often struggle with knowing which theory to apply.

The answers offered at pdfseva are made in a manner that each step is thoroughly and lucidly described. To aid students in better preparing for their board examinations, subject specialists have created the solutions for NCERT Class 10 Math. Not only will these answers be useful for test preparation, but also for completing homework and other tasks.

NCERT texts are often referenced directly or indirectly in questions in the CBSE Class 10 test. As a result, the NCERT Answers for Chapter 6 Triangles of Class 10 Math are among the greatest tools for preparation and equipping oneself to tackle any sort of chapter-related questions in the exam. To succeed in the Class 10 board exams, it is strongly advised that the students regularly practise the NCERT Answers.

Ncert Answers For Chapter 6 Of Math In Class Ten Triangles Thoroughly Explains All The Key Triangle Ideas. You Cannot Directly Measure An Item With The Use Of, Say, A Measuring Tape If You Wish To Determine Its Height Or Its Proportions If It Is Situated At A Distance, Such As The Moon. The Similarity And Congruence Principles Are Used In This Situation. Before Moving On To Subjects Based On These Notions, The Class First Provides An Overview Of Them. This Chapter Focuses On Issues Like Triangle Congruence, Similarity Standards For Them, And How The Pythagoras Theorem May Be Shown Using These Ideas. Many Theorems In Chapter 6 Of The Ncert Solutions For Class 10 Mathematics Will Be Useful In Demonstrating The Triangles’ Congruence And Resemblance.

One Of The Most Fundamental Geometric Forms Is The Triangle, And Research Into Them Has Many Practical Applications. Children Must Thus Carefully Learn This Lesson. By Using The Pertinent Principles To These Diverse Figures, The Topics Covered In This Chapter Will Also Assist Students In Studying Other Forms, Such As Circles, Trapezoids, Rectangles, And Others, And Exploring The Distinction Between Congruence And Resemblance. You May Find A Detailed Pdf Of The Chapter 6 Triangles From The Class 10 Math Ncert Answers Below, As Well As Some Of Them In The Exercises.

List of Formulas in NCERT Solutions Class 10 Maths Chapter 6

NCERT solutions class 10 maths chapter 6 includes a list of important formulas that students need to remember. These formulas can help students solve complex sums related to the triangles with ease. The most important ones are based on the similarity and congruence of different shapes. With the help of these kids can simplify tough questions and solve them quickly. Let us go through the formulas included in the NCERT solutions class 10 maths chapter 6 below:

1. If two triangles, ABC and XYZ, are similar, then the ratio of the sides of these triangles is equal.

E.g., If triangle ABC and XYZ are identical, then AB/XY= BC/YZ= CA/ZX.

2. Inequality: In a triangle, ABC, the sum of two sides is always greater than the third side.

For example : AB+ BC > AC.

3. Area of similar triangles: If two triangles, ABC and XYZ, are similar, then

Area of triangle ABC/ Area of triangle XYZ = (AB)²/ (XY)² = (BC)²/ (YZ)²= (AC)²/ (XZ)²

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