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NCERT Solutions for Maths Class 10 Chapter 6 Exercise 6.1 Triangles - FREE PDF Download
Class 10 Mathematics is a very crucial subject for the students who are about to appear in the board exams. They will learn the new concepts to build a strong foundation to learn the advanced concepts next year at the Higher Secondary level. For this, students need to focus on an important exercise. To make it easier, they can download Exercise 6.1 Class 10 Maths NCERT Solutions prepared by the top teachers of Vedantu. The concepts of this part of the chapter related to triangles have all been properly used to solve the problems more simply. By downloading ex 6.1 class 10 solution, you will become more efficient in using the concepts of geometry.
- 3.1Exercise 6.1
Glance on NCERT Solutions Maths Chapter 6 Exercise 6.1 Class 10 | Vedantu
Exercise 6.1 Class 10 explains the fundamental properties and types of triangles, providing a foundational understanding necessary for further geometric concepts.
It defines triangles as three-sided polygons with three vertices and three angles.
Congruent triangles are covered, focusing on those that have exactly the same size and shape, with corresponding sides and angles being equal.
Similar triangles are also discussed, emphasizing those that have the same shape but may differ in size, with corresponding angles being equal and the ratios of corresponding sides being proportional.
The Pythagorean theorem is introduced, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The exercise includes properties of special triangles, such as isosceles triangles, which have at least two equal sides and angles, and equilateral triangles, which have all three sides and angles equal.
It also explores the criteria for the similarity of triangles, including Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity criteria.
This article contains exercise notes, important questions, exemplar solutions, exercises and video links for exercise 6.1 class 10 - Triangles, which you can download as PDFs.
There are 3 fully solved questions in Chapter 6 Exercise 6.1 Class 10 Triangles.
NCERT Solutions Class 10 Maths Chapter 6 - Triangles Exercise 6.1
ShareShareExercise 6.1
1. Fill in the Blanks Using Correct Word Given in the Brackets:
i. All circles are ______. (congruent, similar)
Ans: Similar.
ii. All squares are ______. (similar, congruent)
Ans: Similar.
iii. All ______ triangles are similar. (isosceles, equilateral)
Ans: Equilateral.
iv. Two polygons of the same number of sides are similar, if their corresponding angles are ______ (equal, proportional)
Ans: Equal
And their corresponding sides are ______. (equal, proportional)
Ans: Proportional.
2. Give Two Different Examples of Pair of -
i. Similar Figures
Ans: The two examples for similar figures are
Two equilateral triangles having sides \[\text{2cm}\] and $\text{4cm}$.
Two squares having sides \[\text{2cm}\] and $\text{4cm}$.
ii. Non-Similar Figures
Ans: The two examples for non - similar figures are
A circle and a square.
A triangle and a rectangle.
3. State whether the following quadrilaterals are similar or not.
Ans: The given quadrilaterals $PQRS$ and $ABCD$ are not similar because their corresponding sides are proportional, that is, $1:2$ but their corresponding angles are not equal.
Conclusion
In conclusion, NCERT Solutions for Maths Exercise 6.1 in Class 10 Chapter 6 - Triangles, provided by Vedantu, offer clear and detailed explanations of the fundamental properties and types of triangles. It is important to focus on understanding the concepts of congruence, similarity, and the Pythagorean theorem. Practicing these solutions of ex 6.1 class 10 helps solidify the foundational principles of triangle geometry, ensuring a strong grasp of the subject. Pay special attention to the criteria for triangle similarity and the application of the Pythagorean theorem in various problems. Regular practice and thorough understanding will greatly aid in mastering this chapter and excelling in exams.
Class 10 Maths Chapter 6: Exercises Breakdown
CBSE Class 10 Maths Chapter 6 Other Study Materials
Chapter-Specific NCERT Solutions for Class 10 Maths
Given below are the chapter-wise NCERT Solutions for Class 10 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
NCERT Study Resources for Class 10 Maths
For complete preparation of Maths for CBSE Class 10 board exams, check out the following links for different study materials available at Vedantu.
FAQs on NCERT Solutions Class 10 Maths Chapter 6 - Triangles Exercise 6.1
1. Why Should You Prefer Vedantu for Class 10 Maths Chapter 6 Ex 6.1 Solution?
The prime reason for choosing Vedantu for downloading Class 10 Maths Ch 6 Ex 6.1 solutions is quality answers and following the CBSE norms strictly. When you use these Class 10 Maths Ex 6.1 solutions to practice, you will become habituated to follow the same rules and score more.
2. How Can You Complete Preparing the Class 10 Maths Exercise 6.1?
Follow the classroom sessions attentively. Solve the exercise first. Download the Exercise 6.1 Class 10 Maths NCERT Solutions and find whether you have solved all the questions correctly or not. Compare your answers and learn how to do it better.
3. How many questions are there in Exercise 6.1 of Chapter 6 of Class 10 Mathematics?
There are three questions in total in the CBSE Exercise 6.1 of Chapter 6 of Class 10 Mathematics. The questions in these exercises are related to similar figures and congruence. To solve this exercise, you can take the help of the NCERT Solution that is available at Vedantu. The NCERT Solutions for Exercise 6.1 of Chapter 6 of Class 10 Mathematics has covered all questions in a precise manner. These answers have been worked out by experts who know how students can score well.
4. What are the examples of Similar Figures in Exercise 6.1 of Chapter 6 of Class 10 Mathematics?
Some of the examples of similar figures are squares, equilateral triangles, and circles. So, if there are two or more circles or squares, or equilateral triangles, you can call them similar figures. Two polygons with the same number of sides are also said to be similar in nature if the corresponding angles are equal and if the corresponding sides are in the same ratio or are proportionate to each other.
5. What is Exercise 6.1 of Chapter 6 of Class 10 Mathematics based on?
Exercise 6.1 of Chapter 6 of Class 10 Mathematics is a short exercise based on the introductory topic of similar figures. The exercise teaches you the difference between similarity and congruence. Students will learn that all congruent figures are similar but not all similar figures may be congruent. Exercise 6.1 also clarifies the conditions for two polygons to be similar. Fill in the blanks or short answer type questions can be asked from this exercise in Class 10 Board examinations.
Vedantu's NCERT Solutions for Exercise 6.1 of Chapter 6 of Class 10 Mathematics provides easy to understand solutions for this exercise on its official website (vedantu.com). The study material provided by Vedantu can be downloaded absolutely free of cost.
6. Is Exercise 6.1 of Chapter 6 of Class 10 Mathematics easy?
Exercise 6.1 of Chapter 6 of Class 10 Mathematics is a piece of cake if you understand the basic concepts taught before the exercise. The exercise contains only 3 questions. These are pretty straightforward and test the direct application of concepts taught for this exercise. Similarity and congruence of circles, triangles, squares, and polygons are the basic principles to be learned for this exercise. Exercise 6.1 is a pretty basic exercise based on the foundational concepts of the chapter.
7. When are two polygons of the same number of sides similar according to Exercise 6.1 of Chapter 6 of Class 10 Mathematics?
Two polygons are said to be similar if they fulfil these two conditions:
Their corresponding angles are equal
Their corresponding sides are in the same proportion (or ratio).
Simple 1 or 2 marks questions can be asked in the exams based on this concept.
Exercise 6.1 has one question (Question 3) based on this principle of similarity of polygons.
The solution to this question is explained step by step with relevant figures here.
8. What topics are covered in Ex 6.1 Class 10 Maths Chapter 6?
Exercise 6.1 covers the fundamental properties of triangles, including definitions, congruence, and similarity. It also introduces the Pythagorean theorem and discusses criteria for triangle similarity. Additionally, ex 6.1 class 10 explores properties of special triangles such as isosceles and equilateral triangles.
9. How does understanding triangle congruence help in solving problems in exercise 6.1 maths class 10 pdf?
Understanding triangle congruence helps students identify when two triangles are identical in shape and size. This knowledge is crucial for solving problems involving corresponding sides and angles. It simplifies proofs and calculations related to triangle geometry in class 10 ex 6.1.
10. What is the significance of the Pythagorean theorem in Class 10 Ex 6.1?
In class 10 maths ch 6 ex 6.1 the Pythagorean theorem is essential for calculating the lengths of sides in right-angled triangles. It states that in such triangles, the square of the hypotenuse equals the sum of the squares of the other two sides. This theorem is frequently applied in various problems within the exercise.
11. How can I determine if two triangles are similar in class 10 maths ch 6 ex 6.1?
Two triangles are similar if their corresponding angles are equal and the ratios of their corresponding sides are proportional. In class 10 maths ex 6.1 can be verified using similarity criteria such as Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS).
12. Why is it important to understand the properties of isosceles and equilateral triangles in class 10 maths chapter 6 exercise 6.1?
Understanding the properties of isosceles and equilateral triangles in class 10 maths chapter 6 exercise 6.1 is important because these triangles have unique characteristics that simplify geometric problem-solving. Recognizing their symmetry and proportionality helps in solving various mathematical problems more easily.
