Chapter 7: Introduction to Euclid’s Geometry Exercise – 7.1
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:
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.
(ii) Collinear points:
Three or more points are said to be collinear if there is a line which contains all of them.
(iii) Parallel lines:
Two lines l and m in a plane are said to be parallel lines if they do not intersect each other.
(iv) Intersecting lines:
Two lines are intersecting if they have a common point. The common point is called point of intersection.
(v) Concurrent lines:
Three or more lines are said to be concurrent if there is a point which lies on all of them.
(vi) Ray:
A line in which one end point is fixed and the other part can be extended endlessly.
(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.
Question: 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
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:
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, AB 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.