Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-7.1, Introduction To Euclid's Geometry, Class 9, Maths

RD Sharma Solutions Ex-7.1, Introduction To Euclid's Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

Q. 1. Define the following terms.

(i)  Line segment                                 

(ii) Collinear points                             

(iii) Parallel lines                                

(iv) Intersecting lines

(v) Concurrent lines

(vi) Ray

(vii) Half-line

Solution

(i) Line-segment:

Give two points A and B on a line I. the connected part (segment) of the line with end points at A and B is called the line segment AB.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(ii) Collinear points:

Three or more points are said to be collinear if there is a line which contains all of them.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(iii) Parallel lines:

Two lines l and m in a plane are said to be parallel lines if they do not intersect each other.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(iv) Intersecting lines:

Two lines are intersecting if they have a common point. The common point is called point of intersection.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(v) Concurrent lines:

Three or more lines are said to be concurrent if there is a point which lies on all of them.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(vi) Ray:

A line in which one end point is fixed and the other part can be extended endlessly.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

(vii) Half-line:

If A, B. C be the points on a line l, such that A lies between B and C, and we delete the point A from line l, the two parts of l that remain are each called half-line.

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

Q. 2. (i) How many lines can pan through a given point?

(ii) In how many points can two distinct lines at the most intersect?

Solution

(i) Infinitely many

(ii) One

Q. 3. (i) Given two points P and Q. Find how many line segments do they determine.

(ii) Name the line segments determined by the three collinear points P. Q and R.

Solution

(i) One

(ii) PQ, QR, PR

 

Q. 4. Write the truth value (T/F) of each of the following statements:

(i) Two lines intersect in a point.

(ii) Two lines may intersect in two points

(iii) A segment has no length.

(iv) Two distinct points always determine a line.

(v) Every ray has a finite length.

(vi) A ray has one end-point only.

(vii) A segment has one end-point only.

(viii) The ray AB is same as ray BA.

(ix) Only a single line may pass through a given point.

(x) Two lines are coincident if they have only one point in common

Solution

(i) False                                  

(ii) False                                 

(iii) False                                

(iv) True                                 

(v) False 

(vi) True 

(vii) False

(viii) False 

(ix) False 

(x) False                             

Q. 5. In the below figure. Name the following:

RD Sharma Solutions Ex-7.1, Introduction To Euclid`s Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics                               

Solution:

(i) Five line segments AB, CD, AC, PQ. DS

(ii) Five rays →PA,→RB,→DC,→QS,→DS

(iii) Four collinear points. C, D, Q, S

(iv) Two pairs of non–intersecting line segments AB and CD, AB and LS.

Q. 6.  Fill in the blanks so as to make the following statements true:

(i) Two distinct points in a plane determine a _____________ line.

(ii) Two distinct ___________ in a plane cannot have more than one point in common.

(iii) Given a line and a point, not on the line, there is one and only _____________ line which passes through the given point and is _______________ to the given line.

(iv) A line separates a plane into _________ parts namely the __________ and the _____ itself.

Solution

(i) Unique

(ii) Lines

(iii) Perpendicular, perpendicular

(iv) Three, two half planes, line.

The document RD Sharma Solutions Ex-7.1, Introduction To Euclid's Geometry, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.
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FAQs on RD Sharma Solutions Ex-7.1, Introduction To Euclid's Geometry, Class 9, Maths - RD Sharma Solutions for Class 9 Mathematics

1. What is Euclid's Geometry?
Ans. Euclid's Geometry refers to the geometrical principles and axioms developed by the ancient Greek mathematician Euclid. It is a branch of mathematics that deals with the study of points, lines, angles, planes, and shapes, based on logical deductions and proofs.
2. Who was Euclid and why is he important in the field of geometry?
Ans. Euclid was an ancient Greek mathematician who is known as the "Father of Geometry." He compiled and organized the existing mathematical knowledge of his time into a systematic and logical framework, known as Euclid's Elements. His work laid the foundation for the study of geometry and his axioms and theorems are still widely used today.
3. What are the key elements of Euclid's Geometry?
Ans. The key elements of Euclid's Geometry include points, lines, angles, planes, and shapes. Euclid's Geometry is based on five fundamental postulates, known as Euclid's axioms, which serve as the foundation for all geometric reasoning and proofs.
4. How did Euclid's Geometry contribute to the development of mathematics?
Ans. Euclid's Geometry had a significant impact on the development of mathematics. It provided a systematic approach to studying geometric shapes and their properties, introducing the concept of logical deductions and proofs. Euclid's axioms and theorems formed the basis for further advancements in geometry and laid the groundwork for other branches of mathematics.
5. Can Euclid's Geometry be applied in real-life situations?
Ans. Yes, Euclid's Geometry has numerous real-life applications. It is used in architecture and construction to design and build structures with precise measurements and angles. It is also used in navigation, surveying, and engineering to determine distances, angles, and shapes of objects. Additionally, Euclid's Geometry is used in computer graphics, computer-aided design (CAD), and many other fields.
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