i) Only one line can pass through a single point.

False because we can draw infinite number of lines through a given point as shown below.

ii) There are an infinite number of lines that pass through two distinct points.

False. According to Axiom 5.1, Given any two distinct points, there is a unique line that passes through them.

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

True. According to Postulate 2, a terminated line can be produced indefinitely.

iv) If two circles are equal, then their radii are equal.

True. According to Postulate 3, A circle can be drawn with any center and any radius.

We know that circles are equal, which means the circles are congruent. (Circles coinciding with each other). This means that circumferences are equal and so the radii of two circles are also equal.

v) In fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.

True. Line segments whose corresponding lengths are equal are equal to one another.

By transitivity law, we know that, if a = b and b = c then a = c.

Here since AB = PQ and PQ = XY therefore, AB = XY according to this law.

Let us consider AB = 5 cm, then PQ will be 5 cm.

But PQ = XY so, XY will also be 5 cm.

Thus, AB = PQ = XY which also implies AB = XY.