Class 9 solutions For Triangle and Its Angles- RD Sharma
FAQs on RD Sharma Class 9 solutions Chapter 9 -Triangle and Its Angles Exercise 9.1 - Free PDF
1. What are the key theorems I need to know to solve questions in RD Sharma Class 9 Maths Chapter 9, Exercise 9.1?
To solve the problems in Exercise 9.1 of 'Triangle and Its Angles', you primarily need to master two fundamental theorems:
- Angle Sum Property of a Triangle: This states that the sum of all three interior angles in any triangle is always 180°.
- Exterior Angle Theorem of a Triangle: This theorem states that if one side of a triangle is extended, the exterior angle formed is equal to the sum of the two opposite interior angles.
The solutions for this exercise provide step-by-step applications of these core principles.
2. How do the RD Sharma solutions for Exercise 9.1 show the correct method for solving problems as per the CBSE pattern?
The solutions follow the standard CBSE pattern by demonstrating a clear, logical progression. For each problem, the method involves:
- Identifying the given information in the triangle.
- Stating the specific theorem being used (e.g., 'By Angle Sum Property').
- Formulating the correct mathematical equation based on the theorem.
- Solving the equation step-by-step to find the unknown angle(s).
This approach ensures you not only get the right answer but also learn how to present it correctly in exams.
3. Why is it important to state the geometric reason for each step while solving problems from this exercise?
Stating the geometric reason (like 'Angle Sum Property' or 'Linear Pair') for each step is crucial for earning full marks in an exam. It shows the examiner that you understand the underlying concepts and are not just guessing. According to the CBSE 2025-26 guidelines, marks are often allocated for both the calculation and the valid reasoning behind it. This practice builds a strong, logical foundation for tackling more complex geometry chapters.
4. What is a common mistake students make when applying the Angle Sum Property, and how can I avoid it?
A common mistake is incorrectly setting up the initial equation, especially when angles are given as algebraic expressions (e.g., 2x, x+10, etc.). Students might forget to equate the sum of these angles to 180°. To avoid this, always start by writing the formula: Angle A + Angle B + Angle C = 180°. Then, substitute the given expressions and solve carefully. The RD Sharma solutions reinforce this correct first step for every problem.
5. How can I decide whether to use the Angle Sum Property or the Exterior Angle Theorem for a specific problem?
The choice of theorem depends on what the question provides and asks for:
- Use the Angle Sum Property when you know two interior angles and need to find the third.
- Use the Exterior Angle Theorem when the problem involves an angle outside the triangle that is formed by extending one of the sides. This is useful when you need to relate an exterior angle to the two opposite interior angles.
In some complex diagrams, you might need to apply both theorems sequentially.
6. How does mastering the concepts in 'Triangle and Its Angles' from the Class 9 syllabus help in Class 10?
The principles from this chapter are foundational for advanced geometry in Class 10. A strong understanding of the Angle Sum Property and Exterior Angle Theorem is essential for topics like:
- Similarity and Congruence Proofs
- Properties of Circles and Tangents
- Introduction to Trigonometry
Mastering these basics in Class 9 ensures you can handle the more complex, multi-step problems in the Class 10 board exams.
7. Can the sum of two angles in a triangle be equal to 180°? Why or why not?
No, the sum of any two angles in a triangle can never be equal to or greater than 180°. According to the Angle Sum Property, the sum of all three angles must be exactly 180°. If two angles were to add up to 180°, the third angle would have to be 0°, which is impossible as it would not form a triangle. Therefore, the sum of any two angles must always be less than 180°.
