RD Sharma Solutions for Class 9 Maths is given here for chapter 7 â€“ Introduction to Euclidâ€™s Geometry. In this exercise, students will study some geometric basic concepts such as point, line and plane. It is not possible to define these three concepts precisely. However, we have a good idea of these concepts by solving exercise 7.1 in Chapter 7. RD Sharma Class 9 solutions help students to practice several questions rigorously to be able to grasp the concepts thoroughly.

## Download PDF of RD Sharma Solutions for Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry Exercise 7.1

### Access Answers to Maths RD Sharma Class 9 Chapter 7 Introduction to Euclid’s Geometry Exercise 7.1 Page number 7.8

### 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 nonâ€“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 nonâ€“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.

## RD Sharma Solutions for Class 9 Maths Chapter 7 Exercise 7.1

RD Sharma Solutions Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry Exercise 7.1 is based on the following topics and subtopics:

- Axioms: The Basic facts which are taken for granted, without proof are called axioms.

**Some important illustrations are:**

-Halves of equal are equal. If a>b and b>c then a>c

-The whole is equal to the sum of its parts and greater than any of its parts.”

- Three basic concepts in geometry, namely, line, point and plane
- Properties of point and lines
- Parallel Lines
- Intersecting Lines
- Line segment
- Interior point of a line segment
- Congruence of line segments
- Length axioms of a line segment
- Line segment length axiom, congruent line segment length axiom, Line segment construction axiom
- Distance between two points
- Mid-point of a line segment
- Ray, Half-line, line separation
- Half-Plane