Question

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 line can be produced indefinitely on both sides.(iv) If two circles are equal, then their radii are equal.(v) if AB=PQ and PQ=XY, then AB=XY.

Answer 1

Complete Question

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 line can be produced indefinitely on both sides.

(iv) If two circles are equal, then their radii are equal.

(v) if AB=PQ and PQ=XY, then AB=XY.

A (i),(ii) - True

(iii),(iv),(v)-False

B(i),(ii),(iii) -True

(iv),(v)-False

C (i),(ii) -False

(iii),(iv),(v)-True

D (i),(ii),(iii) -False

(iv),(v)-True

Answer:

The correct option is C

Explanation:

i is false because several lines can pass through a single point

ii is false because only one line can pass through two distinct points

iii is true because you can extend a line from both points (start and end points )

iv is true because when two equal circle are placed together and radius is trace we will discover that they are equal

v is true because from Euclid's First Axiom , if a= c and c = d the a = d