Question

Identify the symbol of line segments from the following options
$\begin{align}
  & \left[ a \right]\overleftrightarrow{AB} \\
 & \left[ b \right]\overline{AB} \\
 & \left[ c \right]\overrightarrow{AB} \\
 & \left[ d \right]\text{ None of these} \\
\end{align}$

Answer 1

Hint: Solve the question option wise. Recall how the different notations were chosen, and how can we identify from the symbol, what it represents. Hence find which among the options is a representation of a line segment.

Complete step-by-step solution -
Before solving the question, we need to understand the properties of a line segment, a line and a ray.
Line: A line has no endpoints. It extends in both directions, e.g. line AB shown below

Ray: A ray has one endpoint. It extends in one direction only, e.g. Ray AB shown below

Line segment: A line segment has two endpoints. Its length is fixed and does not extend in either direction, e.g. Line segment AB shown below

In symbol form, a mini diagram of line, a ray and a line segment is put over AB to represent line AB, ray AB and line segment AB respectively.
Hence for line AB, we have the symbol $\overleftrightarrow{AB}$, for the ray AB, we have the symbol $\overrightarrow{AB}$ , and for the line segment AB, we have the symbol $\overline{AB}$. Hence option [b] is correct.

Note: Symbols are fundamental in mathematics and play a significant role in making the study of mathematics easy and convenient. Alongside these symbols some other symbols used in geometry are
$\angle $: This is used to represent an angle.
$\bot $: This is the symbol for is perpendicular to.
$\Delta $: This is used to represent a triangle.
$\parallel $: This is the symbol for is parallel to.