Which of the following statements are true and which are false?

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 line can be produced indefinitely on both sides.

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

(v) if AB = PQ and PQ = XY, then AB = XY.

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Explanation:

For (i), In the following figure you can see point P is a common point. There are infinitely many lines passing through point P.

lines passing through point P

For (ii), In the following figure you can see A and B are two distinct points with only one line which passes through two distinct points.

two distinct points

For (iii) In the following figure you can see a terminated line can be produced indefinitely on both sides.

produced indefinitely on both sides

For (iv) If two circles are equal then circles superimpose each other so radii of these type of circles are equal.

For (v) From the following figure it is clear that AB=XY.

figure it is clear that AB=XY

Final Answer: Correct option is C

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