# NCERT Exemplar Class 10 Maths Chapter 6 Solutions: Triangles

NCERT Exemplar Class 10 Maths Solutions Chapter 6 ‘Triangles’ are created at Instasolv to build strong basics in the geometry of triangles. In this chapter of NCERT Class 10 Maths Exemplar, You will be introduced to the concept of similar triangles in this chapter and the different criteria by which the similarities can be established. Basic proportionality theorem, Pythagoras theorem, and several other important theorems are among the topics that are discussed in detail in this NCERT Exemplar problems and solutions for Class 10 Maths Chapter 6. The exemplar problems are crucial for your CBSE exams and building good aptitude for higher studies as well.

57 questions in all have been covered in the 4 broad-ranging exercises of the Exemplar chapter. You will get a plethora of questions covering all the topics across the length and breadth of your syllabus. The questions are arranged in a manner such that their difficulty level will increase as you will proceed in the chapter. This will help you adapt to the increasing complexity of the chapter and help you grasp the gist of the CBSE Class 10 Maths syllabus.

Triangles are an important part of geometry and carry high weightage in the board exams, therefore it is expected of you that you practice it thoroughly. We, at Instasolv, have made sure you miss no chance of amplifying your marks in maths significantly. Our expert maths faculty has left no stones unturned to make the solutions compatible according to your understanding of the subject.

## Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 6: Triangles

**Introduction to the Concept of Similarity**

Two or more polygons can be assumed to be similar when they fulfil the following two conditions:

- Firstly, the corresponding angles in the polygons that are being compared must be equal and their number of sides too.
- Finally, their corresponding sides must be in the same ratio or proportion.

Therefore, we can conclude that when two figures are similar, their shape is the same while their sizes may differ. Another analogy can be that all congruent polygons are similar but all similar polygons are not congruent.

**Basic Proportionality Theorem or Thales Theorem**

According to the Basic Proportionality Theorem, if two triangles have equal angles or are equiangular then the ratio of their corresponding side are always equal.

**Theorem 6.1**

If we will draw a line intersecting two sides of a triangle at different points and which is parallel to the third side, then the first two sides are divided in the same ratio.

**Theorem 6.2**

If two sides of a given triangle are divided into the same ratio by a line, then the line will be parallel to the third side of the same triangle.

**Theorem 6.3 (AAA Criteria)**

When 2 angles are equal to the corresponding two angles of another triangle, then they are similar.

**Theorem 6.4 (SSS Criteria)**

When the 3 corresponding sides of 2 given triangles are in the same ratio, then their angles are equal and they are similar triangles.

**Theorem 6.5 (SAS Criteria)**

When 2 sides of two triangles are in the same ratio and the angle included between the corresponding sides are equal too, then these two triangles are congruent.

**Area of Similar Triangles**

If we take the ratio of the area of similar triangles, it will be equivalent to the square of the ratio of their corresponding sides.

**Pythagoras Theorem**

In a right-angled triangle,

h^{2}=b^{2}+l^{2}, where h is the hypotenuse, b is base, and l is the height of the triangle.

### Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 6: Triangles

- The NCERT Exemplar problems of Class 10 Maths Chapter 6 cover each topic in an elaborate manner.
- Exercise 6.1 is an exercise purely based on multiple-choice questions on topics like similarity of triangles, length of diagonals of a rhombus, etc.
- In Exercise 6.2 there are short answer type questions with reasoning on topics like angles in a triangle, similar triangles, etc.
- The questions in exercise 6.3 are short answer type. You will get to solve diagram-based and word problems both in these exercises.
- The questions in 6.4 will require detailed knowledge of all the theorems of this chapter. Some questions are of miscellaneous nature, that is, they will require the application of multiples theorems to get the desired results.

### Why use NCERT Exemplar Class 10 Maths Solutions Chapter 6: Triangles by Instasolv?

- These solutions to all the NCERT Exemplar Class 10 Maths problems provided to you by Instasolv are ideal for self-study.
- At Instasolv, we have made sure that you get all your queries sorted at just one place.
- By using Instasolv as a source of reference, you will be able to achieve absolute clarity in all the topics of the CBSE Class 10 Maths syllabus.
- The Instasolv platform is aimed at problem-solving in an interactive manner.