Question

Which of the following statements are true and which are false? Give reasons for your answers.
$\left(i\right)$ Only one line can pass through a single point.
$\left(ii\right)$ There are an infinite number of lines which pass through two distinct points.
$\left(iii\right)$ A line can be produced indefinitely on both sides.
$\left(iv\right)$ If two circles are equal, then their radii are equal.
$\left(v\right)$ if $AB=PQ$ and $PQ=XY$, then $AB=XY$.

• A. $\left(i\right),\left(ii\right)$ - True
  $\left(iii\right),\left(iv\right),\left(v\right)$ - False
• B. $\left(i\right),\left(ii\right),\left(iii\right)$ - True
  $\left(iv\right),\left(v\right)$ - False
• C. $\left(i\right),\left(ii\right)$ - False
  $\left(iii\right),\left(iv\right),\left(v\right)$ - True
• D. $\left(i\right),\left(ii\right),\left(iii\right)$ - False
  $\left(iv\right),\left(v\right)$ - True
  

Answer 1

The correct option is C $\left(i\right),\left(ii\right)$ - False

$\left(iii\right),\left(iv\right),\left(v\right)$ - True
(i) Only one line can pass through a single point is false, because there are infinite lines passes through a single point.

(ii) There are an infinite number of lines which pass through two distinct point is false, because through two distinct point only one line can pass .

(iii) A terminated line can be produced indefinitely on both sides is true, because a line can be extended from both sides.

(iv) If two circle are equal then their radii are equal is true, because if two circle are equal then their center is coincide and inscribe equal area thus their radii are equal.

(v) True, according to Euclid's First Axiom, "Things which are equal to the same thing are equal to one another".