RD Sharma Solutions for Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry

RD Sharma Solution for Class 9 Chapter 7 includes several exercises on the of Euclid’s Geometry to help the students practice and learn the concepts of the chapter more effectively. Euclid, a Greek Mathematician employed some of his axioms and theorems to study planes and other solid figures. Euclid’s system is considered an extremely deductive, comprehensive and logical approach towards geometry. Though Euclid’s geometry is also about shapes, lines and angles, the students need to have an in-depth understanding of the topics to be able to understand how the shapes, lines and angles interact with each other.

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Access Answers to Maths RD Sharma Solutions for Class 9 Chapter 7 Introduction to Euclid’s Geometry

Exercise 7.1 Page No: 7.8

Question 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: The part of a line that connects two points or we can say that a shortest distance between the two points. A line segment is one-dimensional.

Here AB is a line segment.

(ii) Collinear points: Two or more points are said to be collinear if all the points lie on same line.

(iii) Parallel lines : Two lines in a plane are said to be parallel lines if they do not intersect each other.

Here l and m are parallel lines.

(iv) Intersecting lines: Two lines are intersecting if they have a common point. The common point is known as point of intersection.

Here l and M are intersecting lines. And P is point of intersection.

(v) Concurrent lines: Two or more lines are said to be concurrent if there is a point which lies on all of them.

Here l, m and n are concurrent lines.

(vi) Ray: A straight line extending from a point indefinitely in one direction only.

Here OA is a ray.

(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 a half-line.

Question 2:

(i) How many lines can pass through a given point?

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

Solution:

(i) Infinitely many

(ii) One

Question 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

Question 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

Question 5: In the below figure, name the following:

(i) Five line segments

(ii) Five rays

(iii) Four collinear points

(iv) Two pairs of non–intersecting line segments

Solution:

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

(ii) Five rays :

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

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

Question 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.

Exercise VSAQs Page No: 7.9

Question 1: How many least number of distinct points determine a unique line?

Solution: Two

Question 2: How many lines can be drawn through both the given points?

Solution: One

Question 3: How many lines can be drawn through a given point?

Solution: Infinite

Question 4: In how many points two distinct lines can intersect?

Solution: One

Question 5: In how many points a line, not in a plane, can intersect the plane?

Solution: One

Question 6: In how many points two distinct planes can intersect?

Solution: Infinite