RD Sharma Solutions Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry
By Swati Singh
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Updated on 29 Apr 2025, 15:42 IST
In this chapter of RD Sharma Solutions for Class 9 Maths, you will find everything you need to understand Euclid’s Geometry with ease. The chapter covers basic concepts like points, lines, and angles based on Euclid's principles.
The solutions offered here are designed to make these ideas easy to understand. With simple explanations and step-by-step guidance, you can learn the main theorems and concepts of Euclidean geometry without any difficulty. These solutions are a great way to build a solid understanding of geometry, which is crucial for your overall math studies.
RD Sharma Solution for Class 9 Chapter 7 - Download PDF
Here are the RD Sharma Solutions Class 9 Maths Chapter 7 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 7 - Question with Answer
RD Sharma Solutions for Class 9 Maths Chapter 7 - Introduction to Euclid’s Geometry, divided into exercises:
RD Sharma Solution for Class 9 Chapter 7 - Question with Answers
1. What is Euclid's first postulate?
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Answer: Euclid's first postulate states that "A straight line can be drawn from any one point to any other point."
2. What is Euclid's second postulate?
Answer: Euclid's second postulate states that "A terminated line can be extended indefinitely."
3. What is Euclid’s third postulate?
Answer: Euclid's third postulate states that "A circle can be drawn with any center and any radius."
4. State Euclid's fourth postulate.
Answer: Euclid's fourth postulate states that "All right angles are equal to one another."
5. What is the fifth postulate of Euclid?
Answer: Euclid's fifth postulate, also known as the parallel postulate, states that "If a line segment falling on two straight lines makes the interior angles on the same side less than two right angles, the two lines, if extended indefinitely, meet on that side."
6. Define a point.
Answer: A point is a precise location in space that has no length, width, or thickness. It is usually represented by a dot.
7. What is a line?
Answer: A line is a straight one-dimensional figure that extends infinitely in both directions. It has no endpoints.
8. What is a line segment?
Answer: A line segment is a part of a line that has two endpoints.
9. What is an angle?
Answer: An angle is formed when two rays (or line segments) meet at a common endpoint called the vertex.
10. What is a right angle?
Answer: A right angle is an angle that measures exactly 90 degrees.
11. What is a straight angle?
Answer: A straight angle is an angle that measures exactly 180 degrees.
12. What is an acute angle?
Answer: An acute angle is an angle that measures less than 90 degrees.
13. What is an obtuse angle?
Answer: An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.
14. What are complementary angles?
Answer: Complementary angles are two angles whose sum is 90 degrees.
15. What are supplementary angles?
Answer: Supplementary angles are two angles whose sum is 180 degrees.
16. Define an equilateral triangle.
Answer: An equilateral triangle is a triangle in which all three sides are equal in length and all angles are 60 degrees.
17. What is a scalene triangle?
Answer: A scalene triangle is a triangle in which all three sides have different lengths and all angles are different.
18. What is an isosceles triangle?
Answer: An isosceles triangle is a triangle in which at least two sides are equal in length, and the angles opposite these sides are equal.
19. 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.
20. What is the difference between a line and a ray?
Answer: A line is a straight path that extends infinitely in both directions, while a ray is a straight path that starts at a point and extends infinitely in one direction.
21. Explain the concept of a parallel line.
Answer: Parallel lines are two lines in a plane that never meet, no matter how far they are extended.
22. What are the different types of angles in terms of their position?
Answer: Angles can be classified as adjacent, complementary, supplementary, or vertical angles based on their position and relationship with other angles.
23. What is the Euclidean method of proof?
Answer: Euclidean method of proof involves deductive reasoning, where conclusions are derived logically from axioms, postulates, and previously established theorems.
24. What are axioms in Euclid’s Geometry?
Answer: Axioms are self-evident truths that do not require proof. In Euclid's Geometry, these are basic assumptions used as the foundation for proving other theorems.
25. What is a polygon?
Answer: A polygon is a closed, two-dimensional figure with straight sides. Examples include triangles, quadrilaterals, pentagons, etc.
26. What is a convex polygon?
Answer: A convex polygon is a polygon where all the interior angles are less than 180 degrees, and no part of the polygon's sides is pushed inward.
27. What is a concave polygon?
Answer: A concave polygon is a polygon that has at least one interior angle greater than 180 degrees, and at least one vertex points inward.
28. How do you construct a perpendicular bisector?
Answer: To construct a perpendicular bisector, place the compass at one end of a line segment, draw arcs above and below the line, repeat from the other end, and connect the intersection points. The line formed is the perpendicular bisector.
29. What is the Pythagorean theorem?
Answer: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).
30. What are congruent figures?
Answer: Two figures are congruent if they have the same shape and size, meaning one can be superimposed on the other.
31. Explain Euclid’s first theorem.
Answer: Euclid's first theorem states that "The whole is greater than the part." This means that if you have a whole object and divide it into parts, the sum of the parts is always less than the whole.
32. What is a transversal line?
Answer: A transversal line is a line that intersects two or more other lines at distinct points.
33. What are alternate interior angles?
Answer: Alternate interior angles are pairs of angles that are on opposite sides of a transversal and between two lines. These angles are equal when the lines are parallel.
34. What are corresponding angles?
Answer: Corresponding angles are angles that are in the same position relative to the transversal and the two lines. These angles are equal when the lines are parallel.
35. What is Euclid's axiom of equality?
Answer: Euclid's axiom of equality states that "Things which are equal to the same thing are also equal to one another."
36. What is the sum of the exterior angles of a polygon?
Answer: The sum of the exterior angles of any polygon, one at each vertex, is always 360 degrees.
37. How do you calculate the sum of interior angles of a polygon?
Answer: The sum of the interior angles of an n-sided polygon is given by the formula (n - 2) × 180°, where n is the number of sides.
38. What is a reflex angle?
Answer: A reflex angle is an angle that measures greater than 180 degrees but less than 360 degrees.
39. What is the angle sum property of a triangle?
Answer: The angle sum property of a triangle states that the sum of the three interior angles of any triangle is always 180 degrees.
40. How do you prove the congruence of two triangles?
Answer: Two triangles are congruent if they satisfy any of the following conditions: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), or RHS (Right angle-Hypotenuse-Side).
RD Sharma Solutions Class 9 Maths Chapter 7 FAQs
What topics are covered in RD Sharma Class 9 Maths Chapter 7?
RD Sharma Class 9 Maths Chapter 7 covers the basics of Euclid’s Geometry, including the five postulates of Euclid, concepts like points, lines, angles, and different types of polygons and triangles. The chapter introduces you to basic geometric principles, properties of angles, and theorems related to parallel lines, as well as congruence and congruent triangles.
How can RD Sharma Solutions for Chapter 7 help me understand Euclid’s Geometry better?
RD Sharma Solutions for Chapter 7 provide step-by-step solutions and detailed explanations of Euclid's postulates and theorems. By breaking down complex concepts into simple steps, these solutions make it easier for students to understand geometric relationships, properties, and proofs. The clear and organized approach helps reinforce learning and comprehension of Euclid’s Geometry.
How should I use RD Sharma Solutions effectively for Chapter 7?
To use RD Sharma Solutions effectively, start by reading the chapter thoroughly, then attempt the exercises on your own. Afterward, refer to the solutions to check your answers and understand the steps involved. Focus on understanding the reasoning behind the proofs and theorems, as well as the applications of Euclid’s postulates in solving problems.
Do RD Sharma Solutions for Chapter 7 include explanations for theorems and proofs?
Yes, RD Sharma Solutions for Chapter 7 include detailed explanations for theorems and proofs. Each theorem is accompanied by a step-by-step proof, making it easier to grasp the logical flow of the reasoning. The solutions also provide practical examples to help you understand how to apply these theorems in various problems.
How are RD Sharma Solutions for Class 9 Maths Chapter 7 helpful for exam preparation?
RD Sharma Solutions for Chapter 7 are highly useful for exam preparation as they provide a clear understanding of the core concepts in Euclid’s Geometry. The solutions help students practice different types of problems and reinforce their understanding of geometric principles, which is crucial for solving exam questions accurately and confidently.