# NCERT Solutions for Class 10 Maths Chapter 6

NCERT Solutions for Class 10 Maths Chapter 6 Triangles all exercises including optional exercise in PDF format for High School UP Board and CBSE Board students. These solutions are useful for Board exams 2021-2022. 10th Maths Chapter 6 Solutions are given in Hindi Medium and English medium free to download or use online. As we know that Utter Pradesh Board also using NCERT Books for their Board exams, so download UP Board Solutions for Class 10 Maths Chapter 6 here free of cost. Download Class 10 Solutions online and offline Apps for 2021-22 based on latest NCERT Solutions. You can share your doubts and ask questions from your classmates through Tiwari Academy Discussion Forum.

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## Class 10 Maths Chapter 6 Triangles Solution

• ### 10th Maths Chapter 6 Exercise 6.6

 Class: 10 Maths (English and Hindi Medium) Chapter 6: Triangles

### 10th Maths Chapter 6 Solutions

NCERT Solutions for class 10 Maths chapter 6 are given for free use. Complete Exercises solutions and a brief description about triangles, similarity of triangles, theorems and the facts related to this chapter are given below. It will help the students to enhance their knowledge about the chapter triangles and the mathematician involved. Download the NCERT Textbooks of all subjects of class 10 updated for 2021-22.

#### Class 10 Maths Chapter 6 Exercise 6.1 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.1 Explanation
Class 10 Maths Chapter 6 Exercise 6.1 Solution

#### Class 10 Maths Chapter 6 Exercise 6.2 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.2 Explanation
Class 10 Maths Chapter 6 Exercise 6.2 Solution

#### Class 10 Maths Chapter 6 Exercise 6.3 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.3 Explanation
Class 10 Maths Chapter 6 Exercise 6.3 Solution

#### Class 10 Maths Chapter 6 Exercise 6.4 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.4 Explanation
Class 10 Maths Chapter 6 Exercise 6.4 Solution

#### Class 10 Maths Chapter 6 Exercise 6.5 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.5 Explanation
Class 10 Maths Chapter 6 Exercise 6.5 Solution

#### Class 10 Maths Chapter 6 Exercise 6.6 Solutions in Videos

Class 10 Maths Chapter 6 Exercise 6.6 Explanation
Class 10 Maths Chapter 6 Exercise 6.6 Solution

### NCERT Solutions for Class 10 Maths Chapter 6

• NCERT Solutions 10th MathsExercise 6.1Read more
• NCERT Solutions 10th MathsExercise 6.2Read more
• NCERT Solutions 10th MathsExercise 6.3Read more
• NCERT Solutions 10th MathsExercise 6.4Read more
• NCERT Solutions 10th MathsExercise 6.5Read more
• NCERT Solutions 10th MathsExercise 6.6Read more

#### OBJECTIVES OF THE CHAPTER – SIMILAR TRIANGLES

• To identify similar figures, distinguish between congruent and similar triangles, prove that if a line is drawn parallel to one side of a triangle then the other two sides are divided in the same ratio, state and use the criteria (Criteria means a standard which is established so that judgement or decision, especially a scientific one can be made) for similarity of triangles viz. AAA, SSS and SAS.
• To verify and use results given in the curriculum based on similarity theorems. To prove the Baudhayan/Pythagoras Theorem and apply these results in verifying experimentally (or proving logically) problems based on similar triangles.
##### History of similar triangles
• A Greek mathematician Thales gave an important relation relating to two equiangular triangles that ‘The ratio of any two corresponding sides in two similar triangles is always the same. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio’. Which is known as the Basic Proportionality Theorem or the Thales Theorem.
• There are so many other important theorems based on similar triangles like If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar. Or if two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar. Download CBSE board Exams papers, for the questions based on BPT in board exams.
###### Historical Facts!
1. Pythagoras theorem is famous because of its wide range of applications. In ancient Indian Mathematics civilization, ‘Sulb Sutras’ written by Bodhayan (800 BC) depict Pythagoras theorem. Bhashkaracharya and Brahmgupta gave different proofs of Pythagoras theorem.
2. Leonardo De Vinchi, the great artist, sculpturist, and architect, famous for his painting ‘Monalisa’ also gave a beautiful proof for this theorem.
3. Thales of Miletus (624 – 546 BC, Greece) was the first known philosopher and mathematician. He is credited with the first use of deductive reasoning in geometry. He discovered many propositions in geometry. He is believed to have found the heights of the pyramids in Egypt, using shadows and principle of similar triangles. Height of pyramids can also be find using applications of trigonometry.
4. Brahma Gupta’s theorem (628 A.D.): The rectangle contained by any two sides of a triangle, is equal to rectangle contained by altitude drawn to the third side and the circum diameter.
5. According to Galileo Galilei, the universe cannot be read until we have learnt the language in which it is written. It is written in mathematical language and the letters are triangles, circles and other geometrical figures, without which it is humanly impossible to comprehend a single word.

##### What is meant by Similarity or Similar Triangle in 10th Maths Chapter6?

According to 10th Maths chapter 6, similarity of geometric figures is an important concept of Euclidean geometry. Similarity in a geometric transformation of one figure into the other figure such that the measure of all linear elements of one figure are in proportion to the corresponding linear elements of the other figure. Two triangles (or any polygons of the same number of sides) are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion). All congruent figures are similar but the similar figures need not be congruent.

##### Which exercise of 10th Maths Chapter 6 is based on Area Theorem?

There are total six exercises in class 10 Maths chapter 6. Out of these exercise 6.4 contains the concepts of Area Theorem. The statement of area theorem is as follow: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

##### How is the Pythagoras theorem useful in 10th Maths chapter 6?

The questions given in exercise 6.5 are based on Pythagoras theorem and its converse. These questions are considered as easier questions if the proof of the theorem is done properly and concept behind the theorem is quite clear. As per theorem, In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The statement must be learnt to the students as it asked to write in examination also.

##### Is optional exercise of class 10 Maths Chapter 6 important for exams?

10th Maths exercise 6.6 is an optional exercise. It is given just for knowledge enhancement not for examination point of view. If a student has done all the other exercises of chapter 6 in 10th Maths, he should try the questions of optional exercise too. It will help to understand the concepts of similarity in better way.

##### In class 10th mathematics, How many exercises, questions and examples are there in chapter 6 Triangles?

There are in all 6 exercises in class 10 mathematics chapter 6 (Triangles).
In first exercise (Ex 6.1), there are only 3 questions.
In second exercise (Ex 6.2), there are in all 10 questions.
In third exercise (Ex 6.3), there are in all 16 questions.
In fourth exercise (Ex 6.4), there are only 9 questions.
In fifth exercise (Ex 6.5), there are 17 questions.
In sixth exercise (Ex 6.6 optional exercise), there are only 10 questions.
So, there are total 65 questions in class 10 mathematics chapter 6 (Triangles).
In this chapter there are in all 14 examples. Examples 1, 2, 3 are based on Ex 6.2, Examples 4, 5, 6, 7, 8 are based on Ex 6.3, Example 9 is based on Ex 6.4 and Examples 10, 11, 13, 14 are based on Ex 6.5.

##### Is there any chapter of class 9th maths which students should revise before starting class 10th maths chapter 6 (Triangles)?

Yes, before starting class 10th mathematics chapter 6 (Triangles), students should revise chapter 7 (Triangles) of class 9th mathematics.

##### How many theorems are there in class 10th Maths chapter 6 Triangles?

There are 9 theorems in chapter 6 (Triangles) of class 10th maths. Theorem 6.1 is known as Basic Proportionality Theorem, Theorem 6.2 is converse of Basic Proportionality Theorem, Theorems 6.3, 6.4 and 6.5 give similarity criterion for two triangles, Theorem 6.8 is known as Pythagoras Theorem and Theorem 6.9 is the converse of Pythagoras Theorem.

##### Which theorem of 10th Maths chapter 6 Triangles is asked for Proof in Exams?

From chapter 6 (Triangles) of class 10 Maths, Proof of Theorem 6.1 (Basic Proportionality Theorem), Theorem 6.3 (area theorem), Theorem 6.8 (Pythagoras Theorem) and Theorem 6.9 (converse of Pythagoras Theorem) can come in exam or you can say that these theorems are important.

##### Which is the easiest exercise of chapter 6 (Triangles) of class 10 math?

Exercise 6.1 is the easiest exercise of chapter 6 (Triangles) of class 10 math.           