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 following figure, if AB = PQ and PQ = XY, then AB = XY.

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 the following figure, if AB = PQ and PQ = XY, then AB = XY.

Answer:

(i)False.

Correct statement

Through a single point, infinite number of lines can pass. 

In above figure, you can see that there are infinite numbers of lines can pass through a single point S.

(ii) False.

Correct statement

through two distinct points, only one line can pass.

In above figure, it can see that there is only one single line that drawn through two

Distinct points R and S

.

(iii) True.

According to Euclid’s laws, A terminated line can be produced indefinitely on both the sides. 

In above figure, you can see there are indefinitely lines both side

(iv)True.

According to axioms 4 of the Euclid, If two circles are equal, then their centre and circumference will coincide and hence, the radii will also be equal.

In above figure, it can see both circle have equal radius  

(v) True.

According to Euclid’s axiom first, things which are equal to the same thing,

And in our given problem it is given that AB and XY are two terminated lines and both are equal to a third line PQ are equal to one another. Therefore, the lines AB and XY will be equal to each other.