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RD Sharma Solutions Class 9 Maths Chapter 9 Triangle and Its Angles
By Swati Singh
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Updated on 29 Apr 2025, 15:41 IST
RD Sharma Solutions are available to help students clear any doubts related to triangles and assist them in solving related problems. These solutions are an excellent resource for consistent practice and can help students achieve high marks in their exams. RD Sharma Solutions for Class 9 Maths Chapter 9 - Triangle and Its Angles includes three exercises, with each question answered by experts.
In this chapter, students will learn about triangles, which are plane figures formed by three non-parallel lines. A triangle is a two-dimensional geometric shape with three sides and three vertices. The three angles of a triangle are formed by its three sides, and the sum of these internal angles always equals 180 degrees. Triangles can be classified based on their angles into: Acute Triangle, Right Angle Triangle, and Obtuse Triangle.
For a more thorough understanding, students can download the PDF of the solutions whenever needed. RD Sharma Solutions serve as a great resource to improve proficiency in Mathematics, as they are crafted according to the latest CBSE syllabus and tailored to suit different learning levels.
RD Sharma Solution for Class 9 Chapter 9 - Download PDF
Here are the RD Sharma Solutions Class 9 Maths Chapter 9 Triangle and Its Angles Solutions, designed to help students prepare effectively for their exams. By referring to these solutions and practicing the problems, students can boost their confidence and improve their scores.
RD Sharma Solution for Class 9 Chapter 9 - Question with Answers
1. What is a triangle?
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Answer: A triangle is a two-dimensional geometric figure formed by three non-parallel lines, with three sides and three vertices.
2. What is the sum of the interior angles of a triangle?
Answer: The sum of the interior angles of a triangle is always 180 degrees.
3. What are the types of triangles based on angles?
Answer: Triangles are classified into three types based on their angles:
Acute Triangle: All angles are less than 90 degrees.
Right Angle Triangle: One angle is exactly 90 degrees.
Obtuse Triangle: One angle is greater than 90 degrees.
4. What is an equilateral triangle?
Answer: An equilateral triangle is a triangle where all three sides are of equal length and all three angles are equal, each measuring 60 degrees.
5. What is an isosceles triangle?
Answer: An isosceles triangle is a triangle that has two sides of equal length, and the angles opposite those sides are also equal.
6. What is a scalene triangle?
Answer: A scalene triangle is a triangle where all three sides have different lengths, and all three angles are of different measures.
7. What is the difference between an acute triangle and an obtuse triangle?
Answer: An acute triangle has all angles less than 90 degrees, while an obtuse triangle has one angle greater than 90 degrees.
8. How do you calculate the third angle of a triangle?
Answer: To calculate the third angle of a triangle, subtract the sum of the two given angles from 180 degrees. For example, if the two angles are 60° and 70°, the third angle is 180° - (60° + 70°) = 50°.
9. What is the Pythagorean theorem?
Answer: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. (a² + b² = c²).
10. What is a right-angled triangle?
Answer: A right-angled triangle is a triangle in which one of the angles is exactly 90 degrees.
11. How do you classify triangles based on sides?
Answer: Triangles can be classified based on sides as:
Equilateral Triangle: All sides are equal.
Isosceles Triangle: Two sides are equal.
Scalene Triangle: All sides have different lengths.
12. What is the angle sum property of a triangle?
Answer: The angle sum property of a triangle states that the sum of the interior angles of any triangle is always 180 degrees.
13. What is an exterior angle of a triangle?
Answer: An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. The exterior angle is equal to the sum of the two non-adjacent interior angles.
14. How do you find the height of a triangle?
Answer: The height of a triangle is the perpendicular distance from a vertex to the opposite side (or its extension). It can be found using the formula: Area = 1/2 × base × height.
15. What is the property of angles opposite to equal sides?
Answer: In an isosceles triangle, the angles opposite the equal sides are also equal.
16. What is the relationship between the sides and angles of a triangle?
Answer: In a triangle, the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest side.
17. What is a median in a triangle?
Answer: A median is a line segment that joins a vertex of the triangle to the midpoint of the opposite side.
18. What is an altitude in a triangle?
Answer: An altitude is a perpendicular line from a vertex to the opposite side (or its extension) of the triangle.
19. What is the centroid of a triangle?
Answer: The centroid is the point where all three medians of the triangle intersect. It divides each median into two parts, with the centroid being two-thirds of the distance from each vertex.
20. What is the orthocenter of a triangle?
Answer: The orthocenter is the point where the altitudes of a triangle intersect.
21. What is the circumcenter of a triangle?
Answer: The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.
22. What is the incenter of a triangle?
Answer: The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.
23. What is the area of a triangle?
Answer: The area of a triangle is given by the formula: Area = 1/2 × base × height.
24. What is the relationship between the angles and sides of an equilateral triangle?
Answer: In an equilateral triangle, all sides are equal, and all angles are 60 degrees.
25. What are the properties of an isosceles triangle?
Answer: In an isosceles triangle, two sides are equal, and the angles opposite these sides are also equal.
26. How can you determine if three sides form a triangle?
Answer: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
27. What is a right triangle's hypotenuse?
Answer: The hypotenuse is the longest side of a right-angled triangle, opposite the right angle.
28. What is the difference between altitude and median?
Answer: An altitude is a perpendicular line from a vertex to the opposite side, while a median connects a vertex to the midpoint of the opposite side.
29. What are the conditions for congruence of triangles?
Answer: The conditions for the congruence of triangles are:
SSS (Side-Side-Side): All three sides of one triangle are equal to the corresponding sides of another triangle.
SAS (Side-Angle-Side): Two sides and the included angle of one triangle are equal to the corresponding parts of another triangle.
ASA (Angle-Side-Angle): Two angles and the included side of one triangle are equal to the corresponding parts of another triangle.
RHS (Right-angle-Hypotenuse-Side): In right-angled triangles, if the hypotenuse and one side are equal, the triangles are congruent.
30. What is the angle sum property of a quadrilateral?
Answer: The sum of the interior angles of any quadrilateral is always 360 degrees.
31. How do you solve for an unknown angle in a triangle using algebra?
Answer: If you know the sum of two angles, subtract that from 180 degrees to find the third angle. For example, if angles are 50° and 60°, the third angle is 180° - (50° + 60°) = 70°.
32. What is a cyclic triangle?
Answer: A cyclic triangle is a triangle whose vertices lie on a single circle.
33. How do you find the perimeter of a triangle?
Answer: The perimeter of a triangle is the sum of the lengths of all its sides.
34. What is the Law of Sines in a triangle?
Answer: The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is constant for all three sides and angles.
35. What is the Law of Cosines in a triangle?
Answer: The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. It is expressed as: c² = a² + b² - 2ab * cos(C).
36. What is a right triangle's area formula?
Answer: The area of a right-angled triangle is given by the formula: Area = 1/2 × base × height, where the base and height are the two perpendicular sides.
37. How do you classify triangles based on their angles and sides?
Answer: Triangles can be classified as:
Acute Triangle: All angles are less than 90°.
Right Triangle: One angle is exactly 90°.
Obtuse Triangle: One angle is greater than 90°.
Equilateral Triangle: All sides and angles are equal.
Isosceles Triangle: Two sides are equal, and two angles are equal.
Scalene Triangle: All sides and angles are different.
38. How do you find the area of an equilateral triangle?
Answer: The area of an equilateral triangle is given by the formula: Area = (√3 / 4) × a², where 'a' is the length of a side.
39. What is the significance of the centroid in a triangle?
Answer: The centroid is the center of mass of a triangle and is the point where all three medians intersect. It divides each median into two parts, with the centroid being two-thirds of the distance from each vertex.
40. What is the importance of the angle sum property in triangles?
Answer: The angle sum property helps to find missing angles in a triangle and is a crucial tool for solving various geometric problems.
RD Sharma Solutions Class 9 Maths Chapter 9 FAQs
Give a brief summary of concepts present in RD Sharma Solutions for Class 9 Maths Chapter 9.
RD Sharma Solutions for Class 9 Chapter 9 focuses on Triangles and Its Angles. It covers the basic properties of triangles, types of triangles based on sides and angles, and the sum of angles in a triangle. The chapter also explains key concepts like the Pythagorean Theorem, exterior angles, and angle sum properties of triangles. Additionally, it discusses congruence of triangles and provides step-by-step solutions to various problems related to these concepts.
Why are RD Sharma Solutions for Class 9 Maths Chapter 9 essential to score high marks in the final exams?
RD Sharma Solutions for Chapter 9 are essential because they help students understand the concepts of triangles and their properties in a structured and clear manner. The solutions provide detailed explanations, step-by-step methods, and plenty of practice problems, which help reinforce learning and improve problem-solving skills. This makes it easier for students to tackle exam questions confidently and score well.
What topics are covered in RD Sharma Class 9 Maths Chapter 9?
RD Sharma Class 9 Maths Chapter 9 covers several important topics, including:
Types of triangles (by sides and angles)
The sum of angles in a triangle
The Pythagorean Theorem
Properties of triangles (including congruence and similarity)
Exterior angles of a triangle
Angle sum property of polygons
Problems based on the above concepts
How can RD Sharma Solutions for Chapter 9 help me understand Triangle and Its Angles better?
RD Sharma Solutions for Chapter 9 provide clear and easy-to-follow explanations for all the concepts related to triangles and angles. By working through the step-by-step solutions, students can develop a solid understanding of the properties of triangles, how to calculate angles, and how to apply the Pythagorean Theorem. The solutions also offer ample practice problems to ensure that students grasp the concepts thoroughly.
How should I use RD Sharma Solutions effectively for Chapter 9?
To use RD Sharma Solutions effectively, start by reading through the chapter and attempting the exercises on your own. After that, refer to the solutions to check your answers and understand the steps involved. Focus on the explanations for theorems and proofs to get a better understanding of the concepts. Regular practice using these solutions will help reinforce your learning and improve your problem-solving skills.
Do RD Sharma Solutions for Chapter 9 include explanations for theorems and proofs related to Triangle and Its Angles?
Yes, RD Sharma Solutions for Chapter 9 include detailed explanations for theorems and proofs related to triangles and angles. Each theorem is explained step-by-step, making it easier for students to understand the reasoning behind the theorems. This helps students not only memorize theorems but also understand their application in solving problems.