1.   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.

i) FALSE
Because there is the infinite number of lines that can be passed through a single point. As shown in the diagram below

ii)  FALSE
Because only one line can pass through two distinct points. As shown in the diagram below

iii)  TRUE
Because a terminated line can be produced indefinitely on both sides. As shown in the diagram below

iv) TRUE
Because if two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal.

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

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