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 figure,if $AB = PQ$ and $PQ = XY,$ then $AB = XY$.

(A-D) $(i)$ False. If we mark a point $O$ on the surface of a paper,we can draw an infinite number of straight lines passing through $O$.
$(ii)$ False. There is one and only one line which passes through two distinct points $P$ and $Q$.
$(iii)$ True. According to Euclid's Postulate $2$,a terminated line can be produced indefinitely.
$(iv)$ True. If two circles are equal,their centers and boundaries coincide when superimposed,so their radii must be equal.
$(v)$ True. According to Euclid's axiom,things which are equal to the same thing are equal to one another.