Q.1. Which of the following statements are true and which are false? Give reasons for your answers.

  1. Only one line can pass through a single point.

  2. There are an infinite number of lines which pass through two distinct points.

  3. A terminated line can be produced indefinitely on both the sides.

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

  5. In the Fig., if AB = PQ and PQ = XY, then AB = XY.

Solution:

  1. False. Infinitely many lines can pass through a point in different directions.

  2. False. Through two distinct points only one line can pass.

  3. True. A terminated line or line segment can be produced indefinitely on both sides to give a line.

  4. True. Two circles of equal area (i.e., equal circles) will have the same radius from the relation area = πr2.

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