Which of the following statements are true and which are false? Give reasons for your
answers.
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 Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.
Answer
(i) False. There can be infinite line drawn passing through a single point.
(ii) False. Only one line can be drawn which passes through two distinct points.
(iii) True. A terminated line can be produced indefinitely on both the sides.
In geometry, a line can be extended in both direction. A line means infinite long length.
(iv) True. If two circles are equal, then their radii are equal.
By superposition, we will find that the centre and circumference of the both circles coincide. Hence, their radius must be equal.
(v) True. By Euclid's first axiom things which are equal to the same thing, are equal to one another.
