# Which of the following statements are true and which are false? Give reasons for your answers.

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

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(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 = πr2

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