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

Answer 1

(i) False. Number of lines can pass through a single point. 

(ii) False. Because there is a unique line that passes through two points. 

(iii)  True. A terminated line can be produced indefinitely on both the sides. 

(iv)  True. Because circumference of equal circles are equal their distance is same from centre. Hence radii of two circles are equal. 

(v)  True. Because E.g., If AB = 4 cm, PQ = 4 cm., then, AB = PQ = 4 cm. 

PQ = XY = 4 cm. 

∴ AB = PQ = XY 

∴ AB = XY.