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

Question

Philoid · Accepted Answer

(i) False

Since, there can be infinite line drawn to be passing through a single point.

(ii) False

Only and only one line can be drawn which passes through two distinct points.

(iii) True

A terminated line can be produced indefinitely on both the sides. A line can be extended in both directions. A line refers to infinite long length

(iv) True

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

By superposition, we will find that the centre and circumference of the both circles coincide. Hence, their radius ought to be equal.

(v) True

By Euclid’s first axiom things which are equal to the same thing, are equal to one another