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By Ankit Gupta
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Updated on 23 Apr 2025, 12:27 IST
Understanding the concept of congruence is an important part of geometry in Class 7 Maths. In Chapter 16 of the RD Sharma textbook, students learn what it means for two shapes to be congruent, how to identify congruent figures, and the rules used to check congruence in triangles. This chapter builds a strong base for students as they move forward in geometry.
The word "congruence" means exactly the same in shape and size. In simple terms, if two figures are congruent, they look alike in every way, even if one is turned or flipped. For example, if you cut out two circles of the same size from paper, they are congruent. This idea is used a lot in real life, such as in designing buildings, making clothes, and even in art.
RD Sharma’s textbook explains this concept clearly with many examples and questions. It starts with basic definitions and slowly introduces methods to check if two figures are congruent. The most important part of the chapter is learning the congruence of triangles. Students are introduced to different rules like SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and RHS (Right angle-Hypotenuse-Side). These rules help us understand when two triangles are congruent just by comparing a few parts of them.
Do Check: RD Sharma Solutions for Class 7 Maths
The RD Sharma Solutions for Chapter 16 are designed to help students understand each topic in a step-by-step way. The solutions follow the latest CBSE guidelines and are written in simple language, making it easy for all students to learn and revise. Each question in the exercise is solved with full explanation, so that students can learn the correct method and also improve their problem-solving skills.
Whether you are preparing for your exams or just want to understand the chapter better, these solutions are a great support. They help clear your doubts and boost your confidence in geometry. By practicing these solutions, you will become better at recognizing congruent figures and solving related problems quickly and correctly.
So, let’s begin the journey into the world of congruent shapes and learn how to master this important chapter with the help of RD Sharma Solutions!
RD Sharma Class 7 Chapter 16 PDF includes detailed solutions, examples, and extra questions to help you master real numbers and other topics. Click here to download the RD Sharma Class 7 Chapter 16 PDF.
In this chapter, students will learn about decimals and how to perform basic operations with them. The solutions provided here are detailed and easy to follow, helping students understand each concept thoroughly.
Q1. Which of the following statements are true or false?
(i) All squares are congruent.
Answer: False.
Explanation: Squares can have different side lengths. Even though all sides in a square are equal, different squares can be of different sizes, so not all are congruent.
(ii) If two squares have equal areas, they are congruent.
Answer: True.
Explanation: Equal areas in squares mean their sides are equal, making the squares congruent.
(iii) If two rectangles have equal areas, they are congruent.
Answer: False.
Explanation: Rectangles with the same area can have different lengths and widths, so they may not be congruent.
(iv) If two triangles have equal areas, they are congruent.
Answer: False.
Explanation: Triangles can have the same area but different side lengths and shapes, so they are not always congruent.
Q2. Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR. Also, AB = PQ and BC = QR. Are the two triangles congruent? If ∠B = 50°, what is the value of ∠R?
Answer: Yes, the triangles are congruent.
Explanation: Since AB = AC, PQ = PR, AB = PQ, and BC = QR, then AC = PR. Hence, ΔABC ≅ ΔPQR by the SSS condition. If ∠B = 50°, then ∠R = 50° as corresponding angles of congruent triangles are equal.
Q3. Triangles ABC and DBC are both isosceles on the same base BC. A and D are on the same side of BC. Are triangles ADB and ADC congruent? If ∠BAC = 40° and ∠BDC = 100°, find ∠ADB.
Answer: Yes, triangles ADB and ADC are congruent.
Explanation: ∠BAC = 40°, so ∠BAD = ∠CAD = 20°. In ΔABC, since it’s isosceles and ∠BAC = 40°, the base angles are 70° each. In ΔDBC, ∠BDC = 100°, so the other angles are 40° each. In ΔADB, we have ∠ABD = 30°, ∠BAD = 20°, hence ∠ADB = 180° - 30° - 20° = 130°.
Q4. AB and CD bisect each other at O. AC and BD are joined to form triangles AOC and BOD. State three matching parts. Are the triangles congruent? Which rule is used?
Answer: Yes, the triangles are congruent.
Explanation: AO = OB, CO = OD, and ∠AOC = ∠BOD (vertically opposite angles). So, ΔAOC ≅ ΔBOD by the SAS rule.
Q5. ΔABC is isosceles with AB = AC. Line AD bisects ∠A and meets BC at D.
(i) Are triangles ADB and ADC congruent?
Answer: Yes, by SAS rule.
(ii) State the matching parts used.
Answer: AB = AC, ∠BAD = ∠CAD, and AD = AD (common side).
(iii) Is BD = DC?
Answer: Yes, because they are corresponding parts of congruent triangles.
Q6. ΔABC is isosceles with AB = AC. AD is perpendicular to BC.
(i) Are triangles ABD and ACD congruent?
Answer: Yes, by RHS rule.
(ii) State the matching parts used.
Answer: AB = AC, AD = AD (common side), and ∠ADB = ∠ADC = 90°.
(iii) Is BD = DC?
Answer: Yes, by corresponding parts of congruent triangles.
Q7. ΔABC is isosceles with AB = AC. AD ⊥ BC. Are triangles ABD and ACD congruent? Which side and angle are equal in both?
Answer: Yes, triangles ABD and ACD are congruent.
Explanation: AB = AC, AD = AD (common side), and ∠ADB = ∠ADC = 90°. By RHS condition, ΔABD ≅ ΔACD. So BD = DC and ∠ABD = ∠ACD.
Chapter 16 is about Congruence, a concept in geometry where two shapes or figures are exactly the same in size and shape. The chapter mainly focuses on understanding congruent figures and proving the congruence of triangles using specific rules.
Congruence is a basic but very useful concept in geometry. It helps students understand how shapes are related to each other. This knowledge is used in higher classes and in real-life situations like architecture, design, and engineering.
The chapter includes:
RD Sharma Solutions are detailed, step-by-step answers to the exercises in the RD Sharma textbook. These solutions help students understand the methods used to solve problems and improve their practice for exams.
Yes, the solutions are written in simple language and explained in a clear manner. Even students who find geometry difficult can follow the steps and learn how to solve each question confidently.
Absolutely! These solutions follow the CBSE pattern and help students prepare well for tests and exams by giving them the correct methods, important tips, and a strong understanding of concepts.
You can find these solutions in printed guidebooks, educational apps, or reliable online learning platforms that offer free or paid access to RD Sharma Solutions for Class 7 Maths.