(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 = πr^{2}.

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