Question

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 Fig., if AB = PQ and PQ = XY, then AB = XY.

Answer 1

(i) False. Infinitely many lines can pass through a point in different directions. 

(ii) False. Through two distinct points only one line can pass. 

(iii) True. A terminated line or line segment can be produced indefinitely on both sides to give a line. 

(iv) True. Two circles of equal area (i.e., equal circles) will have the same radius from the relation area = πr². 

(v) True. From the axiom that if two things are, separately, equal to a third thing, then, they are equal to each other.