"Question 1 Which of the following statements are true and which are false? Give reasons for your answers. (i) Only one line can pass through a single point. (ii) There are an infinite number of lines which pass through two distinct points. (iii) A terminated line can be produced indefinitely on both the sides. (iv) If two circles are equal, then their radii are equal. (v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.
Class 9 - Math - Introduction to Euclid's Geometry Page 85"
Answers
Solution:
i)
False, as there can be infinite number of lines that can be drawn through a single point.
ii)
FALSE , since through two distinct points there can be only one line that can be drawn.
iii)
True , because a line that is terminated can be indefinitely produced on both sides. Since a line can be extended on both its sides infinitely.
Iv
TRUE, because the radii of two circles are equal when the two circles are equal. The circumference and the centre of both the circles coincide; hence the radius of the two circles should be equal.
V
TRUE. According to Euclid’s 1 axiom- “Things which are equal to the same thing are also equal to one another”
Given AB= PQ....(1)
PQ= XY........(2)
From eq 1& 2,
AB=XY [by axiom 1 of Euclid]
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Hope this will help you...
Question :-
1. Which of the following statements are true and which are false? Give reasons for your
(ii) There are an infinite number of lines which pass through two distinct points.
answers.
(1) Only one line can pass through a single point.
(ii) A terminated line can be produced indefinitely on both the sides.
(iv) Iftwo circles are equal, then their radii are equal.
In Fig. 2.9. if AB=PQ and PQ=XY, then AB=XY.
Answer :-
(i) False
Reason : If we mark a point O on the surface of a paper. Using pencil and scale, we can draw infinite number of straight lines passing
through O.
(ii) False
Reason : In the following figure, there are many straight lines passing through P. There are many lines, passing through Q. But there is one and only one line which is passing through P as well as Q.
(iii) True
Reason: The postulate 2 says that “A terminated line can be produced indefinitely.”
(iv) True
Reason : Superimposing the region of one circle on the other, we find them coinciding. So, their centres and boundaries coincide.
Thus, their radii will coincide or equal.
(v) True
Reason : According to Euclid’s axiom, things which are equal to the same thing are equal to one another.
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