Question

Which of the following statements are true and which are false? Give reason for your answers.
(a) Only one line can pass through a single point.
(b) There are an infinite number of lines which pass through two distinct points.
(c) A line can be produced indefinitely on both sides.
(d) If two circles are equal then their radius is equal.
(e) If AB = PQ and PQ = XY, then AB = XY.

Answer 1

Hint: We will look at each of the given points and try to give a good explanation before stating which one true and which one is false or if something has been asked to prove we will also look at that by giving some examples.

Complete answer:
(a) We know that to draw a line we need a point and here we have given only one point so, with just one point we can draw infinitely many lines by taking the other point anywhere.
Hence it is false.

(b) Only one line can be drawn from two points as we have shown in the figure and only one unique slope is possible from two points, hence this statement is false.

(c) The postulate says that "A terminated line can be produced indefinitely." By using this postulate we can say that it is true.
(d) Superimposing the region of one circle on the other, we find them coinciding. So, their centres and boundaries coincide as shown in the figure. Thus, their radii will coincide. Hence true.

(e) According to Euclid's axiom, things which are equal to the same thing are equal to one another. Hence true.

Note: Look at all the reasons carefully while solving this question and one should try to understand them and then only one can understand the true meaning of this question.