RS Aggarwal Class 9 Free PDF Available on Vedantu
FAQs on RS Aggarwal Class 9 Solutions Chapter-9 Congruence of Triangles and Inequalities in a Triangle
1. How do Vedantu's RS Aggarwal Solutions for Class 9 Maths Chapter 9 help with exam preparation for the 2025-26 session?
These solutions provide step-by-step answers to every question in the RS Aggarwal textbook. They are created by subject matter experts to help you understand the correct methodology for proving triangle congruence and solving inequalities. By following these detailed solutions, you can identify weak areas, understand the logic behind complex proofs, and strengthen your problem-solving approach for the CBSE exams.
2. What are the key congruence criteria I need to master for solving problems in RS Aggarwal Chapter 9?
To successfully solve the problems in this chapter, you must be proficient in applying the five main congruence criteria. The solutions clearly demonstrate how to use:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
RHS (Right angle-Hypotenuse-Side) for right-angled triangles.
Each solution in our guide explicitly states the criterion used for a particular problem.
3. How do I correctly apply the ASA (Angle-Side-Angle) criterion when solving problems in this chapter?
To correctly apply the ASA criterion, you must demonstrate that two angles and the side included between them in one triangle are equal to the corresponding two angles and included side in another. For instance, to prove ΔABC ≅ ΔPQR using ASA, you must establish that ∠B = ∠Q, BC = QR, and ∠C = ∠R. The side must be the one connecting the vertices of the two angles. Our solutions show this precise correspondence for each relevant problem.
4. Why is writing the congruence of triangles in the correct corresponding order (e.g., ΔABC ≅ ΔPQR) so important?
Writing the congruence in the correct corresponding order (e.g., A ↔ P, B ↔ Q, C ↔ R) is fundamental because it directly defines which sides and angles are equal. This concept is often called CPCTC (Corresponding Parts of Congruent Triangles are Congruent). An incorrect order, like ΔABC ≅ ΔQRP, would imply a different set of corresponding parts, leading to flawed proofs and incorrect conclusions, which would lose marks in an exam.
5. What is the main difference between the types of problems in Exercise 9A and Exercise 9B of this chapter?
The exercises in Chapter 9 are structured to build your understanding progressively. Here's the focus of each:
Exercise 9A primarily deals with proving the congruence of triangles using the SSS, SAS, ASA, AAS, and RHS criteria.
Exercise 9B shifts focus to the properties of inequalities in a triangle. Problems here involve proving relationships such as 'the angle opposite the longer side is greater' or 'the sum of any two sides of a triangle is greater than the third side'.
6. What are the most common mistakes to avoid when solving problems on congruence of triangles from Chapter 9?
A very common mistake is attempting to use SSA or ASS (Side-Side-Angle) as a congruence rule; it is not a valid criterion and will lead to an incorrect proof. Another frequent error is failing to correctly match the corresponding vertices when stating the final congruence relation. Always double-check that your proof follows a logical sequence and that each statement is supported by a valid geometric reason.
7. How do the solutions for Chapter 9 explain the theorems on inequalities in a triangle?
The solutions for the inequalities section explain key theorems by applying them to specific problems. They offer clear, step-by-step proofs for concepts such as:
The angle opposite the longer side is larger.
The side opposite the larger angle is longer.
The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
Working through these solved examples helps in mastering the construction of proofs for inequality-based questions.
8. Why is it necessary to provide a reason for every step when writing a geometric proof for congruence?
Providing a reason (e.g., 'Given', 'Common Side', 'Vertically Opposite Angles', 'by SAS criterion') for each statement is essential for building a logical and verifiable argument. It shows the examiner that you understand the underlying theorems and postulates. As per the CBSE 2025-26 marking scheme, marks are often allocated for both the correct statement and its corresponding valid reason. Omitting reasons will result in a loss of marks, even if your final conclusion is correct.
9. When should I specifically use the RHS (Right angle-Hypotenuse-Side) criterion to prove congruence?
The RHS criterion is a special case applied exclusively to right-angled triangles. You should use it only when you can establish that in two right-angled triangles:
The hypotenuses are equal (H).
One pair of other corresponding sides is equal (S).
If you have information about an included angle or another angle, you might use SAS or AAS instead. The solutions clearly indicate when RHS is the most efficient method.
