Question

Which of the following is not possible to construct ?

• A.
  A line into two equal parts
• B.
  A line segment into 4 equal parts
• C.
  Angle bisector of an angle
• D.
  
  A triangle having angles in the ratio 1 : 1 : 2

Answer 1

The correct option is A

A line into two equal parts
$\Rightarrow$ Consider the first statement :
As we already know, a line has no definite length that means it can be extended infinitely in any direction. So a line cannot be divided into two parts as it does not have a definite length.
$\Rightarrow$ Statement is incorrect.

$\Rightarrow$ Now, consider 2nd statement i.e. Option (b)
As, line segment has definite length like 12 cm, 15 cm, 10 cm, So we can divide it into 4 parts.

$\Rightarrow$ statement is correct.

$\Rightarrow$ Now, let us check 3rd statement.
As we already know that, we can draw the angle bisector of an angle.
$\Rightarrow$ Statement is correct.

$\Rightarrow$ Now, let us check 4th statement.
$x+x+2x={180}^{\circ }\Rightarrow 4x={180}^{\circ }\Rightarrow x={45}^{\circ }{45}^{\circ },{45}^{\circ },{90}^{\circ }$
$\Rightarrow$ Statement is correct.

So, we can conclude that option (a) is correct.
Therefore,
$\Rightarrow \text{Option (a) A line into two equal parts.}$