RD Sharma Solutions Class 9 Maths Chapter 14 – Free PDF Download
RD Sharma Solutions for Class 9 Maths Chapter 14 - Quadrilaterals consists of problems based on a polygon with four vertices (corners) and four sides, known as a quadrilateral. A quadrilateral has four interior angles, and the sum of these angles is always 360 degrees. For example, consider a quadrilateral PQRZ, with angles P, Q, R, and Z. The sum of these angles is expressed as ∠P + ∠Q + ∠R + ∠Z = 360°.
To gain a better understanding of these concepts, students are advised to practice RD Sharma Solutions regularly.
Quadrilaterals can be classified based on their intersecting nature. If the quadrilateral does not intersect, it is called a simple quadrilateral. If the quadrilateral self-intersects, it is a complex quadrilateral. Simple quadrilaterals can be further classified into concave and convex quadrilaterals, depending on the position of their diagonals and interior angles.
The RD Sharma Class 9 Solutions thoroughly explain all the concepts from the chapter on quadrilaterals, following the CBSE syllabus 2025-26.
RD Sharma Solution for Class 9 Chapter 14 - Download PDF
RD Sharma Solutions Class 9 Maths Chapter 14- Quadrilateral in Two Variables 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 14 - Question with Answers
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1. What is a quadrilateral?
Answer: A quadrilateral is a polygon with four sides, four vertices, and four angles.
2. What is the sum of the interior angles of a quadrilateral?
Answer: The sum of the interior angles of a quadrilateral is 360 degrees.
3. If three angles of a quadrilateral are 110°, 50°, and 40°, what is the fourth angle?
Answer: The fourth angle is 160°, as 110° + 50° + 40° + x = 360°, so x = 360° - 200° = 160°.
4. In a quadrilateral, if the angles are in the ratio 1:2:4:5, what are the measures of each angle?
Answer: Let the angles be x, 2x, 4x, and 5x. The sum is 360°, so x + 2x + 4x + 5x = 360°, giving x = 30°. Therefore, the angles are 30°, 60°, 120°, and 150°.
5. What defines a convex quadrilateral?
Answer: A convex quadrilateral is one where all interior angles are less than 180°, and the diagonals lie inside the figure.
6. What defines a concave quadrilateral?
Answer: A concave quadrilateral has at least one interior angle greater than 180°, and at least one diagonal lies outside the figure.
7. What is a parallelogram?
Answer: A parallelogram is a quadrilateral where opposite sides are parallel and equal in length.
8. What are the properties of a parallelogram?
Answer: In a parallelogram, opposite sides are equal, opposite angles are equal, diagonals bisect each other, and adjacent angles are supplementary.
9. What is a rectangle?
Answer: A rectangle is a parallelogram with four right angles.
10. What are the properties of a rectangle?
Answer: In a rectangle, opposite sides are equal, all angles are 90°, and diagonals are equal in length.
11. What is a rhombus?
Answer: A rhombus is a parallelogram with all sides equal in length.
12. What are the properties of a rhombus?
Answer: In a rhombus, opposite angles are equal, diagonals bisect each other at right angles, and diagonals bisect the angles.
13. What is a square?
Answer: A square is a rectangle with all sides equal in length.
14. What are the properties of a square?
Answer: In a square, all sides are equal, all angles are 90°, and diagonals are equal and bisect each other at right angles.
15. What is a trapezium?
Answer: A trapezium is a quadrilateral with one pair of opposite sides parallel.
16. What is the area of a parallelogram?
Answer: The area of a parallelogram is the base multiplied by the height (Area = base × height).
17. What is the area of a rectangle?
Answer: The area of a rectangle is length multiplied by width (Area = length × width).
18. What is the area of a rhombus?
Answer: The area of a rhombus is half the product of its diagonals (Area = ½ × diagonal₁ × diagonal₂).
19. What is the area of a square?
Answer: The area of a square is the square of its side length (Area = side²).
20. What is the area of a trapezium?
Answer: The area of a trapezium is half the product of the sum of its parallel sides and its height (Area = ½ × (a + b) × height), where a and b are the lengths of the parallel sides.
21. How do you prove that a quadrilateral is a parallelogram?
Answer: A quadrilateral is a parallelogram if both pairs of opposite sides are equal in length.
22. How do you prove that a quadrilateral is a rectangle?
Answer: A quadrilateral is a rectangle if it is a parallelogram with one right angle.
23. How do you prove that a quadrilateral is a rhombus?
Answer: A quadrilateral is a rhombus if its diagonals bisect each other at right angles.
24. How do you prove that a quadrilateral is a square?
Answer: A quadrilateral is a square if it is a rectangle with all sides equal.
25. What is the mid-point theorem for a trapezium?
Answer: The mid-point theorem states that the line joining the midpoints of the non-parallel sides of a trapezium is parallel to the parallel sides and its length is half the sum of the lengths of the parallel sides.
26. What is the condition for a quadrilateral to be cyclic?
Answer: A quadrilateral is cyclic if the sum of each pair of opposite angles is 180°.
27. What is the relation between the diagonals of a rhombus?
Answer: The diagonals of a rhombus bisect each other at right angles and divide the rhombus into four right-angled triangles.
28. How do you find the perimeter of a quadrilateral?
Answer: The perimeter of a quadrilateral is the sum of the lengths of all its sides.
29. How do you find the area of a quadrilateral using diagonals?
Answer: The area of a cyclic quadrilateral can be calculated using Brahmagupta's formula, which involves the lengths of the sides and the semiperimeter.
30. What is the significance of the angle sum property in quadrilaterals?
Answer: The angle sum property helps in determining unknown angles in a quadrilateral, aiding in its classification and area calculations.
Chapter 14 of RD Sharma's Class 9 Mathematics textbook, titled "Quadrilaterals," plays a pivotal role in building a strong foundation in geometry.This chapter delves into the properties, classifications, and area calculations of various quadrilaterals, which are fundamental concepts in both academic assessments and real-world applications.
Importance of RD Sharma Class 9 Math's Chapter 14
- Fundamental Geometric Concepts: Understanding the properties of quadrilaterals enhances spatial reasoning and geometric visualization skills, which are essential for higher studies in mathematics and related fields.
- Preparation for Advanced Topics: The knowledge gained from this chapter serves as a prerequisite for more advanced topics such as coordinate geometry, trigonometry, and calculus, where geometric principles are extensively applied.
- Real-World Applications: The concepts learned are applicable in various professions, including architecture, engineering, and computer graphics, where the understanding of shapes and their properties is crucial.
- Enhanced Problem-Solving Skills: Regular practice of exercises in this chapter improves analytical thinking and problem-solving abilities, which are beneficial for competitive exams and logical reasoning tests.
FAQs on RD Sharma Solutions Class 9 Maths Chapter 14
How are the RD Sharma Solutions for Class 9 Maths Chapter 14 helpful to score high marks among CBSE students?
RD Sharma Solutions for Chapter 14 provide step-by-step explanations and a variety of practice problems, enhancing conceptual clarity and problem-solving skills. Regular practice using these solutions helps students build confidence and perform well in exams.
Which is the toughest topic in Maths Class 9?
The difficulty of topics varies among students, but many find Coordinate Geometry, Mensuration, and Surface Area and Volume challenging due to their complex concepts and calculations.
Is it important to practice RD Sharma Solutions for Class 9 Maths Chapter 14 on a daily basis?
Yes, consistent practice is crucial. Daily practice of RD Sharma Solutions helps reinforce concepts, improve speed and accuracy, and prepare effectively for exams.
Is Class 9 Maths tough?
Class 9 Maths introduces new concepts that may seem challenging initially. However, with regular practice and a clear understanding of fundamentals, students can find the subject manageable and even enjoyable.
What are the key benefits of RD Sharma Solutions for Class 9 Maths Chapter 14?
The key benefits include:
Comprehensive coverage of quadrilateral properties and theorems.
Detailed solutions that clarify complex concepts.
Variety of problems to enhance problem-solving skills.
Alignment with CBSE syllabus, ensuring exam relevance.
Who is the father of mathematics?
Archimedes is often referred to as the "father of mathematics" due to his significant contributions to geometry, calculus, and fluid mechanics.